Question
Solve for all values of xx by factoring.
x, squared, plus, 10, x, minus, 40, equals, 4, x
x
2
+10x−40=
4x
x, squared, plus, 10, x, minus, 40, equals, 4, x
x
2
+10x−40=
4x
Answers
GPT-4o mini
To solve the equation \( x^2 + 10x - 40 = 4x \) by factoring, we first rearrange the equation to one side:
\[
x^2 + 10x - 40 - 4x = 0
\]
This simplifies to:
\[
x^2 + 6x - 40 = 0
\]
Next, we want to factor the quadratic equation \( x^2 + 6x - 40 \). We need to find two numbers that multiply to \(-40\) (the constant term) and add to \(6\) (the coefficient of the linear term).
The two numbers that satisfy this condition are \(10\) and \(-4\):
\[
10 \times (-4) = -40 \quad \text{and} \quad 10 + (-4) = 6
\]
Now, we can factor the quadratic:
\[
(x + 10)(x - 4) = 0
\]
Next, we set each factor equal to zero:
1. \( x + 10 = 0 \)
\[
x = -10
\]
2. \( x - 4 = 0 \)
\[
x = 4
\]
Thus, the solutions to the equation \( x^2 + 10x - 40 = 4x \) are:
\[
\boxed{-10} \quad \text{and} \quad \boxed{4}
\]
\[
x^2 + 10x - 40 - 4x = 0
\]
This simplifies to:
\[
x^2 + 6x - 40 = 0
\]
Next, we want to factor the quadratic equation \( x^2 + 6x - 40 \). We need to find two numbers that multiply to \(-40\) (the constant term) and add to \(6\) (the coefficient of the linear term).
The two numbers that satisfy this condition are \(10\) and \(-4\):
\[
10 \times (-4) = -40 \quad \text{and} \quad 10 + (-4) = 6
\]
Now, we can factor the quadratic:
\[
(x + 10)(x - 4) = 0
\]
Next, we set each factor equal to zero:
1. \( x + 10 = 0 \)
\[
x = -10
\]
2. \( x - 4 = 0 \)
\[
x = 4
\]
Thus, the solutions to the equation \( x^2 + 10x - 40 = 4x \) are:
\[
\boxed{-10} \quad \text{and} \quad \boxed{4}
\]