Question

Which equation would you get by completing the square and factoring the equation below?

x2 + 10x + 16 = 0

A. (x - 5)(x - 5) = -9
B. (x + 10)(x + 10) = -25
C. (x + 5)(x + 5) = 9
D. (x + 10)(x - 10) = 0

Answer 1

I had a typo: *x^2

Answer 2

Guidance:
1. Add 9 to both sides
2. Transform the right side into a square binomial
3. Take square root of both sides
4. Isolate x

Answer 3

To complete the square and factor, you look for what we need to satisfy the x term. Since it's 10x, we know that we are going to (x+5)(x+5) to get 10x as the middle term when we multiply it out. There is only one solution that has that....

but to finish the square we now need the constant to equal 5*5 or 25. to do this we add 9 and subtract 9 so we have
\[x^{2}+10x +25 -9\]
factoring it we get
(x+5)(x+5) - 9 = 0
(x+5)(x+5)= 9

Answer 4

Thank you! :D