Question

What equation results from completing the square and then factoring? x2 + 10X = 15

Answer 1

Answer:

C) (x + 5)² = 40

Step-by-step explanation:

Given the quadratic equation, x² + 10x = 15:

To complete the square, take the coefficient of the middle term (b), and divide it by 2a:

x² + 10x + $[\frac{b}{2a}]^{2}$  = 15 + $[\frac{b}{2a}]^{2}$

x² + 10x + $[\frac{10}{2}]^{2}$  = 15 + $[\frac{10}{2}]^{2}$  

x² + 10x + 5²  = 15 + 5²

x² + 10x + 25 = 40

The trinomial on the left-hand side of the equation provides a perfect square binomial factors: u² + 2uv + v² = (u + v)²

x² + 10x + 25 = 40

(x + 5)²  = 40

Therefore, the correct answer is Option C)  (x + 5)²  = 40