Math Problem Solver

Solve by factoring:

Transform the equation such that one side is equal to zero. $$\begin{aligned} {x}^{2} &= 169 \\ x^{2} - 169 &= 0\end{aligned}$$

Factor the nonzero side of the equation completely. $$\begin{aligned} x^{2} - 169 &= 0 \\ \left(x - 13\right) \left(x + 13\right) &= 0\end{aligned}$$

The product of any number and zero is zero, so the equation will hold true if either of the factors is equal to zero. Set each of the factors equal to zero and solve. $$\begin{aligned} x - 13 &= 0\\ x &= 13\end{aligned}$$ $$\begin{aligned} x + 13 &= 0\\ x &= -13\end{aligned}$$

Take the square root of both sides of the equation $$\begin{aligned}x^{2} &= 169 \\ \sqrt{x^{2}} &= \sqrt{169} \end{aligned}$$

Remember that both positive and negative numbers will result in a positive number when squared, so a square root will have both a positive and a negative answer. $$\begin{aligned}x &= \pm 13 \\ x = 13 &,\, x=-13\end{aligned}$$