Question

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

Answer 1

C) (x + 5)² = 40

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 +
`[(b)/(2a)]^(2)` = 15 +
`[(b)/(2a)]^(2)`

x² + 10x +
`[(10)/(2)]^(2)` = 15 +
`[(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