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