Question

The sum of a number and it’s square is 30 Find the numbers

Answer 1

The sum of a number and it’s square is 30

$x+x^2=30$

Steps to find x.

1. subtract 30 from both sides and simplify

$\begin{gathered} x+x^2-30=30-30 \\ x^2+x-30=0 \end{gathered}$

2. use the quadratic formula

$x=\frac{-b\pm\sqrt[]{b^2-4\cdot\: a\cdot c}}{2\cdot\: a}$$x_{1,\: 2}=\frac{-1\pm\sqrt{1^2-4\cdot\:1\cdot\left(-30\right)}}{2\cdot\:1}$

3. Solve for the positive value

$x_1=\frac{-1+11}{2\cdot\:1}=5$

4. so the answer is number 5