Question

Eight increase by the square of a number is five times the difference of the number and 2

Answer 1

Answer:

$x=\frac{5\pm\sqrt{47}i}{2}$

Step-by-step explanation:

Given : Expression 'eight increase by the square of a number is five times the difference of the number and 2'

To find : Write ans solve the expression ?

Solution :

Let the number be 'x',

Eight increase by the square of a number i.e. $x^2+8$

Five times the difference of the number and 2 i.e. $5(x-2)$

Expression is written as

'eight increase by the square of a number is five times the difference of the number and 2'

$x^2+8=5(x-2)$

Solving the expression,

$x^2+8=5x-10$

$x^2-5x+18=0$

Using quadratic formula, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, a=1 , b=-5 and c=18.

$x=\frac{-(-5)\pm\sqrt{(-5)^2-4(1)(18)}}{2(1)}$

$x=\frac{5\pm\sqrt{25-72}}{2}$

$x=\frac{5\pm\sqrt{-47}}{2}$

$x=\frac{5\pm\sqrt{47}i}{2}$