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Solve the quadratic function by completing the square. What are the missing pieces in the steps?

–32 = 2(x2 + 10x)

–32 + _____ = 2(x2 + 10x + 25)

18 = 2(x + 5)2

9 = (x + 5)2

± _____ = x + 5

x = –2 or x = ____


_____=missing pieces

Verified Answer :

Neuron

If you would like to solve the quadratic function by completing the square, you can do this using the following steps:

- 32 = 2(x^2 + 10x)
- 32 + 50 = 2(x^2 + 10x + 25)
18 = 2(x + 5)^2
9 = (x + 5)^2
± sqrt(9) = x + 5
± 3 = x + 5
x = - 2 or x = - 8

The steps used in completing the square of the given quadratic equation have been detailed below.

How to complete the square of quadratic Equations?

The first step given is;

- 32 = 2(x² + 10x)

The next step is to add a square of half the coefficient of x. Which in this case is 50 to both sides.

Second step is;

-32 + 50 = 2(x² + 10x + 25)

Third step is to further simplify the left and favtorize the right to get;

18 = 2(x + 5)²

9 = (x + 5)²

Fourth step is to take square root of both sides to get;

±√9 = x + 5

±3 = x + 5

Thus;

x = - 2 or x = - 8

Read more about completing the square at; https://brainly.com/question/10449635

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