Question

Let ​x^2+10x=6.

What values make an equivalent number sentence after completing the square?
Enter your answers in the boxes.
x^2+10x+___=___

Answer 1

x² + 10x + 25 = 31

Explanation:

To complete the square use half the x coefficent (10/2 = 5)

and square it (5² = 25)

Then add it to both sides

x² + 10x + 25 = 6 + 25

x² + 10x + 25 = 31

Answer 2

x^2 + 10x + 25 = 31

Explanation:

x^2 + 10x + (10/2)^2 = 6 + 25

x^2 + 10x + 25 = 6 + 25

x^2 + 10x + 25 = 31

The first step requires a bit of explanation. The way to complete the square is to take 1/2 the linear term (10x) and square it

1/2 10 = 5

5 squared = 25

That number must be added to the right side to maintain equality.