Question

what are the solutions to $x^2 + 8x + 7 = 0$?
$\bigcirc$ $x = -8$ and $x = -7$
$\bigcirc$ $x = -7$ and $x = -1$
$\bigcirc$ $x = 1$ and $x = 7$
$\bigcirc$ $x = 7$ and $x = 8$

Explanation:

Step1: Factor the quadratic equation

We factor \(x^{2}+8x + 7\). We need two numbers that multiply to \(7\) and add up to \(8\). The numbers are \(7\) and \(1\), so we can write the equation as \((x + 7)(x+1)=0\).

Step2: Solve for x

Using the zero - product property, if \((x + 7)(x + 1)=0\), then either \(x+7 = 0\) or \(x + 1=0\).

• For \(x+7=0\), we subtract \(7\) from both sides: \(x=-7\).
• For \(x + 1=0\), we subtract \(1\) from both sides: \(x=-1\).

Answer:

\(x=-7\) and \(x = - 1\) (corresponding to the option: \(x=-7\) and \(x=-1\))