1. x=3 or x=-1
Step-by-step explanation:
1. x^2 -2x -3 =0 .
The product is -3 while the sum is -2. We determine two numbers whose product is -3 and sum -2. The two numbers are -3 and 1. The next step is to replace -2x in the equation with these two values; x^2 +x -3x -3 =0. Factoring yields; x(x+1) -3(x+1) =0. Upon simplification this becomes; (x-3)(x+1) =0. This implies that either; x-3 =0 or x+1 =0. Solving for x yields; x=3 or x=-1
Q2 Solution:
x = -1/2 or x = 3
Step-by-step explanation:
2x²-5x-3 =0
In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -5 and their product 2(-3)=-6. By trial and error the two numbers are found to be; -6 and 1. The next step is to split the middle term by substituting it with the above two numbers found;
2x²-6x+x-3 = 0
2x(x-3)+1(x-3) = 0
(2x+1)(x-3) = 0
2x+1 = 0 or x-3 = 0
2x = -1 or x = 3
x = -1/2 or x = 3 are the solutions of the given quadratic equation.
Q3 Soution:
x = 4 or x = 3
Step-by-step explanation:
x²-7x = -12
x²-7x+12 = 0
In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -7 and their product 12. By trial and error the two numbers are found to be; -4 and -3. The next step is to split the middle term by substituting it with the above two numbers found;
x²-4x-3x+12 = 0
x(x-4)-3(x-4) = 0
(x-4)(x-3) = 0
x-4 = 0 or x-3 = 0
x = 4 or x = 3 are the solutions of the given quadratic equation.
Q4:
x = -2/3 or x = 6
Step-by-step explanation:
3x² = 16x+12
3x²-16x-12 = 0
In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -16 and their product 3(-12)= -36. By trial and error the two numbers are found to be; -18 and 2. The next step is to split the middle term by substituting it with the above two numbers found;
3x²-18x+2x-12 = 0
3x(x-6)+2(x-6) = 0
(3x+2)(x-6) = 0
3x+2 = 0 or x-6 =0
3x = -2 or x = 6
x = -2/3 or x = 6 are the solutions of the given quadratic equation.
Q5:
x = 6 or x = -4
Step-by-step explanation:
x²-2x-24 = 0
In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -2 and their product -24. By trial and error the two numbers are found to be; -6 and 4. The next step is to split the middle term by substituting it with the above two numbers found;
x²-6x+4x-24 = 0
x(x-6)+4(x-6) = 0
(x-6)(x+4) = 0
x-6 = 0 or x+4 = 0
x = 6 or x = -4 are the solutions to the given quadratic equation.
Q6:
x = 4/3 or x = -1
Step-by-step explanation:
3x² = x+4
3x²-x-4 = 0
In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -1 and their product -12. By trial and error the two numbers are found to be; -4 and 3. The next step is to split the middle term by substituting it with the above two numbers found;
3x²-4x+3x-4 = 0
x(3x-4)+1(3x-4) =0
(3x-4)(x+1) = 0
3x-4 =0 or x+1 =0
3x = 4 or x = -1
x = 4/3 or x = -1
