Question

What are the solutions to the following equation?
`{x}^(2) + 8x + 15 = 0`

Answer 1

The solutions to the given quadratic equation are;

`\begin{gathered} x=-3 \\ \text{and} \\ x=-5 \end{gathered}`

Step-by-step explanation:

Given the quadratic equation in the attached image.

`x^2+8x+15=0`

to solve for x, let us factorize the equation;

`\begin{gathered} x^2+8x+15=0 \\ x^2+3x+5x+15=0 \\ x(x+3)+5(x+3) \\ (x+3)(x+5)=0_{} \end{gathered}`

So, we have;

`\begin{gathered} x+3=0 \\ x=-3 \\ or \\ x+5=0 \\ x=-5 \end{gathered}`

Therefore, the solutions to the given quadratic equation are;

`\begin{gathered} x=-3 \\ \text{and} \\ x=-5 \end{gathered}`