Question

Solve for all values of xx by factoring.
x, squared, plus, 2, x, minus, 80, equals, 0
x
2
+2x−80=
0

Answer 1

To solve the quadratic equation \( x^2 + 2x - 80 = 0 \) by factoring, we first need to find two numbers that multiply to \(-80\) (the constant term) and add up to \(2\) (the coefficient of the \(x\) term).

The two numbers that satisfy these conditions are \(10\) and \(-8\) since:

- \(10 \times -8 = -80\)
- \(10 + (-8) = 2\)

Now we can rewrite the quadratic equation using these two numbers:

\[
x^2 + 10x - 8x - 80 = 0
\]

Next, we can group the terms:

\[
(x^2 + 10x) + (-8x - 80) = 0
\]

Factoring out the common terms in each group gives:

\[
x(x + 10) - 8(x + 10) = 0
\]

Now, factor out \((x + 10)\):

\[
(x + 10)(x - 8) = 0
\]

To find the values of \(x\), we set each factor to zero:

1. \(x + 10 = 0 \Rightarrow x = -10\)
2. \(x - 8 = 0 \Rightarrow x = 8\)

Thus, the solutions to the equation \(x^2 + 2x - 80 = 0\) are:

\[
\boxed{-10} \quad \text{and} \quad \boxed{8}
\]