Answer :
Answer:
The solutions to the given quadratic equation are;
[tex]\begin{gathered} x=-3 \\ \text{and} \\ x=-5 \end{gathered}[/tex]Explanation:
Given the quadratic equation in the attached image.
[tex]x^2+8x+15=0[/tex]to solve for x, let us factorize the equation;
[tex]\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}[/tex]So, we have;
[tex]\begin{gathered} x+3=0 \\ x=-3 \\ or \\ x+5=0 \\ x=-5 \end{gathered}[/tex]Therefore, the solutions to the given quadratic equation are;
[tex]\begin{gathered} x=-3 \\ \text{and} \\ x=-5 \end{gathered}[/tex]