Question

solve for all values of x by factoring. x² + 10x - 40 = 4x

Explanation:

Step1: Rearrange the equation to standard quadratic form

Subtract \(4x\) from both sides to get \(x^{2}+10x - 4x-40 = 0\), which simplifies to \(x^{2}+6x - 40=0\).

Step2: Factor the quadratic equation

We need two numbers that multiply to \(- 40\) and add up to \(6\). The numbers are \(10\) and \(- 4\) because \(10\times(-4)=-40\) and \(10+( - 4)=6\). So the factored form is \((x + 10)(x-4)=0\).

Step3: Solve for \(x\) using the zero - product property

If \((x + 10)(x - 4)=0\), then either \(x+10 = 0\) or \(x - 4=0\).

• For \(x+10 = 0\), subtract \(10\) from both sides: \(x=-10\).
• For \(x - 4=0\), add \(4\) to both sides: \(x = 4\).

Answer:

\(x=-10\) or \(x = 4\)