Question

50 points and brainliest fo the first correct solutions

Answer 1

Qn 9.

9. x =0 or x = -3/2

Step-by-step explanation:

9.  4x^2 +6x =0. The first step is to factor x;

x(4x+6) =0.

This implies that either;

x=0 or 4x+6 =0.

Solving for x yields;

4x =-6 which upon dividing both sides by 4 becomes x =-3/2.  

x =0 or x = -3/2 are the solutions to the given quadratic equation.

Qn 10.

10. x =0 or x =3

Step-by-step explanation:

10.  7x^2 =21x.

The equation can be rewritten as;

7x^2 -21x =0.

We note that 7x is a common multiple and we factor it out;

7x(x-3)=0. This implies that either;

7x =0 or x-3 =0. Solving 7x =0 yields;

x=0. Solving x-3 = 0 yields;

x =3.

x =0 or x =3 are the solutions to the given quadratic equation

Qn 11.

11. x = -9 or x = 5

Step-by-step explanation:

11.  (x+2)^2 =49.

The equation is already in factored form. The next step is to obtain square roots on both sides of the equation which yields;

(x+2) =±7. This implies that;

x = -2±7.

x = -9 or x = 5 are the solutions to the given quadratic equation.

Qn 12.

12.  x =3/8 or x = -1/3.

Step-by-step explanation:

12.  x+3 =24x^2.

The first step is to write the equation in the standard form;

24x^2 -x -3 =0.

The next step we make the coefficient of x^2 equal to 1 by diving all through by 24;

x^2 -(1/24)x - (1/8) =0.

Consequently, we determine two numbers whose sum is -(1/24) and their product -(1/8). By trial and error the two numbers are found to be; -(3/8) and (1/3). The equation is then re-written as;

x^2 +(1/3)x -(3/8)x -(1/8) =0. The equation is then factored as;

x(x +1/3) -3/8 (x +1/3) =0. Upon simplification this becomes;

(x -3/8)(x +1/3) =0. Implying that;

x =3/8 or x = -1/3 are the solutions to the given quadratic equation.

Qn 13.

13.  x =2.5 or x = -2

We plot the individual functions using the Desmos graphing utility; an online graphing tool. Consequently we determine the x-intercept which represents the zeros of the given function;

The graphical solutions to the first equation are; x =2.5 or x = -2.

Qn. 14

The graphical solutions to the this equation are; x =3.5 or x = -1.33.

Qn. 15

The graphical solutions to the this equation are; x =0.42 or x = -7.17.

Qn. 16

The graphical solutions to the this equation are; x =3.25 or x = -2.

Qn. 17

The graphical solutions to the this equation are; x =4.5 or x = -0.67.

Qn. 18

The graphical solutions to the this equation are; x =0.46 or x = -2.71.

Qn .19

19.  x^2 +x -20 =0.

Step-by-step explanation:

If 4 and -5 are the solutions to a quadratic equation, this implies;

x =4 or x = -5.

Consequently;

x -4 =0 or x +5 =0.

(x -4)(x+5) =0.

Opening the brackets and simplifying yields;

 x^2 +x -20 =0.

Qn. 20

20.  x^2 +6x  =0

Step-by-step explanation:

If -6 and 0 are the solutions to a quadratic equation, then;

x =-6 or x = 0.

This implies that;

x +6 =0 or x =0.

Consequently;

x(x+ 6) =0

Opening the brackets and simplifying yields;

 x^2 +6x  =0.

Qn. 21

21.  x^2 -11x +24 =0

Step-by-step explanation:

If 3 and 8 are the solutions to a quadratic equation, then;

x =3 or x = 8.

This implies that;

x -3 =0 or x -8 =0.

Consequently;

(x -3)(x -8) =0

Opening the brackets and simplifying yields;  

x^2 -11x +24 =0.

Answer 2

Answer to Q9:

{0,-3/2}

Step-by-step explanation:

We have given an equation.

4x² + 6x = 0

We have to solve above equation for the value of x.

Taking 2x common from given equation, we have

2x(2x+3) = 0

Applying Zero-Product Property , we have

2x = 0 or 2x+3 = 0

x = 0 or 2x = -3

x = 0 or x = -3/2  

Hence, the solution of given equation is {0,-3/2}.

Answer to Q10:

{0,3}

Step-by-step explanation:

We have given an equation.

7x² =21x

We have to solve above equation for the value of x.

Adding -21x to both sides of above equation, we have

7x²-21x = 21x-21x

7x²-21x = 0

Taking 7x common from above equation, we have

7x(x-3) = 0

Applying Zero-Product Property , we have

7x = 0 or x-3 = 0

x = 0 or x = 3  

Hence, the solution of given equation is {0,3}.

Answer to Q11:

{5,-9}.

Step-by-step explanation:

We have given an equation.

(x+2)² = 49

We have to solve above equation for the value of x.

Taking square root to both sides of above equation, we have

√(x+2)² = √49

x+2 = ±7

Adding to -2 to both sides of above equation, we have

x+2-2 = ±7-2  

x = 7-2 or x = -7-2

x = 5 or x = -9

Hence, the solution of given equation is {5,-9}.

Answer to Q12:

{1/2,-1/3}

Step-by-step explanation:

We have given an equation.

x+3 = 24x²

24x²-x-3 = 0

We use method of factorization to solve this.

Splitting the middle term of given equation so that the sum of two term should be -1 and their product be -72, we have

24x²-9x+8x-3 = 0

Taking common, we have

3x(8x-3)+1(8x-3) = 0

Taking (8x-4) as common, we have

(8x-4)(3x+1) = 0

Applying Zero-Product Property to above equation, we have

8x-4 = 0 or 3x+1 = 0

8x = 4 or 3x = -1

x = 4/8 or x = -1/3

x = 1/2 or x =-1/3

Hence, the solution of given equation is {1/2,-1/3}.

Answer to Q13:

(2.5,0) and (2,0)

Step-by-step explanation:

We have given an quadratic equation.

2x²-x-10 = 0

We have to solve above equation by method of graphing.

We have plotted the graph of given equation.

Finding the x-intercepts of equation, we have  

(2.5,0) and (2,0)

Hence, x-intercepts are the solution of given equation.

Answer to Q14:

(-1.33,0) and (3.5,0)

Step-by-step explanation:

We have given an quadratic equation.

6x²-13x = 28

6x²-13x-28 = 0

We have to solve above equation by method of graphing.

We have plotted the graph of given equation.

Finding the x-intercepts of equation, we have  

(-1.33,0) and (3.5,0)

Hence, x-intercepts are the solution of given equation.

Answer to Q15:

(-7.17,0) and (0.42,0)

Step-by-step explanation:

We have given an quadratic equation.

4x²+27x = 12

4x²+27x-12 = 0

We have to solve above equation by method of graphing.

We have plotted the graph of given equation.

Finding the x-intercepts of equation, we have

(-7.17,0) and (0.42,0)

Hence, x-intercepts are the solution of given equation.

Answer to Q16:

(-2,0) and (3.25,0)

Step-by-step explanation:

We have given an quadratic equation.

4x²-5x-26 = 0

We have to solve above equation by method of graphing.

We have plotted the graph of given equation.

Finding the x-intercepts of equation, we have  

(-2,0) and (3.25,0)

Hence, x-intercepts are the solution of given equation.

Answer to Q17:

(-.67,0) and (4.5,0)

Step-by-step explanation:

We have given an quadratic equation.

6x²-23x = 18

6x²-23x-18 = 0

We have to solve above equation by method of graphing.

We have plotted the graph of given equation.

Finding the x-intercepts of equation, we have  

(-.67,0) and (4.5,0)

Hence, x-intercepts are the solution of given equation.

Answer to Q18:

(-2.77,0) and (.46,0)

Step-by-step explanation:

We have given an quadratic equation.

-4x²-9x+5 = 0

We have to solve above equation by method of graphing.

We have plotted the graph of given equation.

Finding the x-intercepts of equation, we have  

(-2.77,0) and (.46,0)

Hence, x-intercepts are the solution of given equation.

Answer to Q19:

x²+x-20 = 0

Step-by-step explanation:

We have given the solution of equation.  

4 and -5  

We have to find the equation of given solution.

x = 4 and x = -5

Hence, x-4 = 0 and x +5 = 0

For equation,

(x-4)(x+5) = 0

x²-4x+5x-20 = 0

x²+x-20 = 0 which is the answer.

Answer to Q20:

x²+6x = 0  

Step-by-step explanation:

We have given the solution of equation.  

-6 and 0

We have to find the equation of given solution.

Hence, x = -6 and x = 0

x+6 = 0 and x = 0

x(x+6) = 0

Distribute x over parentheses,

x²+6x = 0 which is the answer.

Answer to Q21:

x²-11x+24 = 0

Step-by-step explanation:

We have given the solution of equation.

3 and 8

We have to find the equation of given solution.

x = 3 and x = 8

x-3 = 0 and x-8 = 0

(x-3)(x-8) = 0

x²-3x-8x+24 = 0

Adding like terms, we have

x²-11x++24 = 0 which is the answer.