Question

Solve$x^2-7x-30=0\text{.}$

Short answer

The solution of the given equation is and $x=-3andx=10.$

Step-by-step solution

Step 1. Given information

The given equation is $x^2-7x-30=0$

We have to find the solution of the equation i.e the value of $x$that satisfies the given equation.

Step 2. Form the factors

$\begin{array}{l}\text{Thegivenequationis}{x}^2-7x-30=0.\\ \Rightarrow x^2-7x-30=0\\ \Rightarrow x^2+3x-10x-30=0\left[\text{Splitthemiddleterm}\right]\\ \Rightarrow x\left(x+3\right)-10\left(x+3\right)=0\left[\text{Takeoutthecommonterms}\right]\\ \Rightarrow \left(x-10\right)\left(x+3\right)=0\left[\text{Formthefactors}\right]\end{array}$

Step 3. Solve for x

$\begin{array}{l}\text{Byzeroproductrule,}\\ \Rightarrow x-10=0\\ \Rightarrow x=10\\ \text{and,}\\ \Rightarrow x+3=0\\ \Rightarrow x=-3\\ \text{Thesolutionsetis}\left\{-3,10\right\}\end{array}$