Question

question
solve for all values of ( x ) by factoring.
( x^2 + 8x - 24 = 3x )

Explanation:

Step1: Rearrange the equation

Subtract \(3x\) from both sides to get the quadratic equation in standard form \(ax^2 + bx + c = 0\).
\(x^2 + 8x - 24 - 3x = 0\)
Simplify the like terms: \(x^2 + 5x - 24 = 0\)

Step2: Factor the quadratic

We need two numbers that multiply to \(-24\) and add up to \(5\). The numbers are \(8\) and \(-3\) because \(8\times(-3)=-24\) and \(8 + (-3)=5\).
So, we can factor the quadratic as \((x + 8)(x - 3)=0\)

Step3: Solve for \(x\)

Set each factor equal to zero and solve for \(x\).

• For \(x + 8 = 0\), subtract \(8\) from both sides: \(x = -8\)
• For \(x - 3 = 0\), add \(3\) to both sides: \(x = 3\)

Answer:

The solutions are \(x = -8\) and \(x = 3\)