Question

Solve for all values of xx by factoring.
x 2 +10x−40=4x

Answer 1

To solve the equation \( x^2 + 10x - 40 = 4x \) by factoring, we first need to rearrange the equation so that one side equals zero.

Starting with the initial equation:
\[
x^2 + 10x - 40 = 4x
\]

Subtract \( 4x \) from both sides:
\[
x^2 + 10x - 4x - 40 = 0
\]

This simplifies to:
\[
x^2 + 6x - 40 = 0
\]

Next, we will factor the quadratic equation \( x^2 + 6x - 40 \). We need to find two numbers that multiply to \(-40\) (the constant term) and add up to \(6\) (the coefficient of the linear term).

The numbers \(10\) and \(-4\) satisfy these conditions:
\[
10 \cdot (-4) = -40 \quad \text{and} \quad 10 + (-4) = 6
\]

Thus, we can factor the quadratic:
\[
(x + 10)(x - 4) = 0
\]

Now, we can set each factor equal to zero:
1. \( x + 10 = 0 \)
2. \( x - 4 = 0 \)

Solving each equation gives:
1. \( x = -10 \)
2. \( x = 4 \)

Thus, the solutions are:
\[
\boxed{-10} \quad \text{and} \quad \boxed{4}
\]