Darrell tried to solve the equation x2 + 10x = -9 by completing the square. His work and some of his answers are shown below. Each red blank, marked with a le

Question

Darrell tried to solve the equation x2 + 10x = -9 by completing the square. His work and some of his answers are shown below. Each red blank, marked with a le

Answer 1

x² + 10x = -9

 

 

When completing the square, we want the left side of the equation to be a trinomial that is a product of a perfect square. Let's look at the first and second terms of the left side.  10x is half of 5x.  Also, x*x is x².  Therefore, the square will be (x + 5)².  The last term of the square is 25.  So we need to add 25 on both sides of equation to make the left side a perfect square.

 

x² + 10x + 25 = -9 + 25

 

(x + 5)(x + 5) = -9 + 25

 

(x + 5)² = 16

 

 

Square-root both sides of equation.

 

x + 5 = ±√(16)

x = -5 ± √(16)

 

x = -5 + √(16)             and         x = -5 - √(16)

 

x = -5 + 4                    and         x = -5 - 4

 

x = -1                          and         x = -9