Question

Given the equation x2+10x+25=0, what are the solutions?

A) x=−5
B) x=5
C) x=−10
D) x=10

Answer 1

The solution to the quadratic equation x²+10x+25=0 is x=-5, which is found by factoring the perfect square trinomial. The correct option is A) x=-5.

Step-by-step explanation:

The equation x²+10x+25=0 is a quadratic equation in the form ax²+bx+c=0, where a, b, and c are constants. To find the solutions for x, we can factor the equation since it is a perfect square trinomial. Factoring the equation gives us (x+5)(x+5)=0, which further simplifies to x+5=0. Therefore, the solution to the equation is x=-5, which means that the correct option is A) x=-5.

To check our solution, we can substitute x=-5 back into the original equation. This will give us (-5)² + 10(-5) + 25 = 0, which simplifies to 25 - 50 + 25 = 0, confirming that x=-5 is indeed the solution to the equation.