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)=(-1\pm√(1^2-4\cdot\:1\cdot\left(-30\right)))/(2\cdot\:1)`

3. Solve for the positive value

`x_1=(-1+11)/(2\cdot\:1)=5`

4. so the answer is number 5