Final answer:
To create a quadratic equation with only one solution at x = -5, we can use the perfect square trinomial (x + 5)², resulting in the quadratic equation x² + 10x + 25 = 0.
Step-by-step explanation:
To create a quadratic equation of the form ax² + bx + c = 0 that has only one solution, x = -5, we need to ensure that the discriminant (the part of the quadratic formula under the square root, b² - 4ac) equals zero. For a quadratic equation to have only one solution, it must be a perfect square trinomial.
If we let a be 1 (although any non-zero value would work), we can find b and c by considering that x + 5 is a factor of the trinomial squared. So, we have (x + 5)² = x² + 10x + 25. This gives us the quadratic equation:
x² + 10x + 25 = 0
where a = 1, b = 10, and c = 25. This satisfies the original requirement because the discriminant is 0, which means there is exactly one real solution.