Question

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

Answer 1

ANSWER

• x = -2

,

• x = 10

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=\frac{8\pm12}{2}$

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

$x=\frac{8-12}{2}=\frac{-4}{2}=-2$

and the other when adding 12:

$x=\frac{8+12}{2}=\frac{20}{2}=10$

So the number is either -2 or 10.