Question

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 =
Intro
Done

Answer 1

x = -2; or x = -8

Explanation:

Solve the quadratic function by completing the square. What are the missing pieces in the steps? -32=2(x^2+10)

-32+___=2(x2+10x+25)

18=2(x+5)^2

9=(x+5)^2

+-___=x+5

X=-2 or x=___

Solution:

From the first line:

-32+___=2(x2+10x+25)

Also, in the second line:

18=2(x+5)^2

Let the missing piece on line 2 be a, hence:

x² + 10x + 25 = (x + 5)² and -32 + a = 18

a = 18 + 32 = 50

-32 + 50 =2(x²+10x+25)

18 = 2(x+5)²

Dividing through by 2:

18 / 2= [2(x+5)² / 2]

9 = (x + 5)²

Taking square root of both sides:

√9 = √(x + 5)²

± 3 = x+5

Simplifying the equation to get:

3 = x + 5; -3 = x + 5

x = 3 - 5; or x = -3 - 5

x = -2; or x = -8