Question

solve the equation by graphing the related function
$x^2 + 5x = 0$

select the correct choice and, if necessary, fill in the answer box to complete your choice

a the solution(s) is/are $x = $
(simplify your answer. use a comma to separate answers as needed.)

b the equation has no solution.

Explanation:

Step1: Identify related function

The related function is $f(x) = x^2 + 5x$

Step2: Find x-intercepts (roots)

Factor the function: $x(x + 5) = 0$
Set each factor to 0:
$x = 0$ or $x + 5 = 0$
Solve for x: $x = 0$ or $x = -5$

Step3: Match to graph

The first graph crosses the x-axis at $x=0$ and $x=-5$, confirming the roots.

Answer:

A. The solution(s) is/are x = 0, -5