Question

The square of a number is 20 more than 8 times the number.find the number.

Answer 1

• x = -2

,

• x = 10

Step-by-step explanation

Let 'x' be the number. The square of a number is x². Then that equals to 8 times the number (8x) plus 20. Therefore we have the equation

`x^2=8x+20`

We can rewrite this equation as follows:

`x^2-8x-20=0`

And use the quadratic formula to determine the number:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

In this case, a = 1, b = -8 and c = -20:

`x=\frac{8\pm\sqrt[]{8^2-4\cdot1\cdot(-20)}}{2\cdot1}`
`x=\frac{8\pm\sqrt[]{64^{}+80}}{2}`
`x=\frac{8\pm\sqrt[]{144}}{2}`
`x=(8\pm12)/(2)`

We have two posible results for this number. One when subtracting 12:

`x=(8-12)/(2)=(-4)/(2)=-2`

and the other when adding 12:

`x=(8+12)/(2)=(20)/(2)=10`

So the number is either -2 or 10.