1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Yuri [45]
3 years ago
14

Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation?

Mathematics
2 answers:
REY [17]3 years ago
8 0

Answer:

The solution set of the equation are (2,0) and (-12,0)

Step-by-step explanation:

Given : Equation x^2+10x=24

To find : Solve equation by completing the square ?

Solution :

The general form of quadratic equation is ax^2+bx+c=0

So, x^2+10x-24=0

To complete the square we add and subtract (\frac{b}{2})^2

i.e. (\frac{b}{2})^2=(\frac{10}{2})^2=5^2

Applying in equation,

x^2+10x-24+5^2-5^2=0

Re-writ equation as,

x^2+2\times 5\times x+5^2-24-25=0

Apply a^2+2ab+b^2=(a+b)^2

(x+5)^2-49=0

(x+5)^2=49

Taking root both side,

x+5=\pm \sqrt{49}

x+5=\pm 7

x+5=7 or x+5=-7

x=2 or x=-12

Therefore, the solution set of the equation are (2,0) and (-12,0)

IrinaVladis [17]3 years ago
7 0
\large\begin{array}{l} \textsf{So the question gives us this equation:}\\\\ \mathsf{x^2+10x=24}\\\\ \mathsf{x^2+2\cdot 5x=24}\\\\ \textsf{In order to complete the square on the left side, just add }\mathsf{5^2}\\\textsf{to both sides of the equation above:}\\\\ \mathsf{x^2+2\cdot 5x+5^2=24+5^2}\\\\ \mathsf{x^2+5x+5x+5^2=24+25}\\\\ \mathsf{x(x+5)+5(x+5)=49} \end{array}

\large\begin{array}{l} \mathsf{(x+5)(x+5)=49}\\\\ \mathsf{(x+5)^2=49}\\\\\\ \textsf{So,}\\\\ \mathsf{x+5=\pm\,\sqrt{49}}\\\\ \mathsf{x+5=\pm\,7}\\\\ \mathsf{x=\pm\,7-5} \end{array}

\large\begin{array}{l} \begin{array}{rcl} \mathsf{x=-7-5}&~\textsf{ or }~&\mathsf{x=7-5}\\\\ \mathsf{x=-12}&~\textsf{ or }~&\mathsf{x=2} \end{array}\\\\\\ \textsf{Solution set: }\mathsf{S=\{-12,\,2\}.}\qquad\checkmark \end{array}


If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2170326


\large\textsf{I hope it helps. :-)}


Tags: <em>solve quadratic equation completing square solution algebra</em>

You might be interested in
Craig Browning bakes cookies for the elementary school cookie sale. His chocolate chip cookies sell for $1.00 a dozen, and his o
Volgvan

Answer and Step-by-step explanation:

Let

Number of chocolate chip cookies = x

Number of oatmeal brownie cookies = y

Bake chocolate chip cookies up to 20 dozen = x≤ 20

Bake oatmeal brownies up to 40 dozen= y≤40

Total cookies = x + y ≤ 50

Number of oatmeal brownie will be no more than three times the number of chocolate chip= y≤3x

From the inequality:

                        X + y=50                          

                         y = 3x

By putting the value of y, we get

    x + 3x = 50

     4x = 50

    X = 12.5

By putting the value of x=12.5 in equation y = 3x, we get

Y = 3(12.5)

    = 37.5

Craig should make 12.5 dozen chocolate chip and 37.5 dozen oatmeal brownies in order to make more money.

8 0
3 years ago
What is quarter past 3
svetlana [45]
What is quarter pass 3 your answer would be 3:45
7 0
3 years ago
Read 2 more answers
What answer would you choose in this case the 1 2 3 or 4
VMariaS [17]
The Answer Is B.

To Find The Mean, You Add Up Every Number And Divide By How Many Numbers There Were.

136 + 145 + 123 + 140 + 126 = 670

670 Divided By 5 = 134

The Mean For The 4 Weeks Was 136.
The Mean For The 5 Weeks Was 134.

The Mean Decreased By 2. Your Answer Is B.
6 0
4 years ago
Evaluate 5w-w/x when w=6 and x=2
Rudiy27

Answer:

27

Step-by-step explanation:

5×6-(6/2)

=30-3

=27

3 0
3 years ago
Read 2 more answers
ali sorced 66 and 72 marks respectively. for his two tests what is the lowest marks he must have sorced for his third test if an
dimaraw [331]

Answer:

87

Step-by-step explanation:

66 + 72 + 87 = 225

225 / 3 = 75

6 0
2 years ago
Other questions:
  • If a ball is thrown directly upward with a velocity of 34 ft/s, its height (in feet) after t seconds is given by y = 34t − 16t2.
    14·1 answer
  • Find n. Perimeter = 46 in.<br>8 in.​
    5·1 answer
  • Kelly spends $63.90 on items for a party. She buys thank you cards that cost $5.40 (including tax). She also buys gift bags that
    15·2 answers
  • What are the x-intercept and y-intercept of the graph of y=13x−6 ?
    7·1 answer
  • Answer the following questions CORRECTLY I will know if this is wrong. I WILL REPORT ANY INCORRECT ANSWERS!
    9·1 answer
  • What is 3 made into a fraction
    12·2 answers
  • Salim walked113miles to school and then212miles to work after school. How far did he walk in all? 316 miles 325 miles 345 miles
    10·1 answer
  • 7. Calculate the volume of the triangular prism on the right.
    8·1 answer
  • Need help on this problem
    9·1 answer
  • pleeeeeeeeeeeease hellllllllp meeeeeee the circle has a center of 0.its raduis is 3 cm,and the central angle A measures 100.what
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!