Question

Solve the equation by factoring. $$x^{2}-5 x=84$$

Short answer

The solutions to the equation \(x^{2}-5x=84\) are \(x=12\) and \(x=-7\).

Step-by-step solution

Rearrange the equation

Rearrange the given equation \(x^{2}-5x=84\) to the standard form of a quadratic equation \(ax^{2} + bx + c = 0\). In this case, it becomes \(x^{2}-5x-84=0\)

Factorize

Factorize the quadratic polynomial \(x^{2}-5x-84\). The factors will be \((x–12)(x+7)=0\) since -12 and 7 add up to -5 and multiply to -84.

Solve for x

Setting each of the factors to zero gives the solutions to the equation. Solve the equations \(x–12=0\) and \(x+7=0\) separately. One will get \(x=12\) and \(x=-7\).