Answer:
[tex]x=\frac{5\pm\sqrt{47}i}{2}[/tex]
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. [tex]x^2+8[/tex]
Five times the difference of the number and 2 i.e. [tex]5(x-2)[/tex]
Expression is written as
'eight increase by the square of a number is five times the difference of the number and 2'
[tex]x^2+8=5(x-2)[/tex]
Solving the expression,
[tex]x^2+8=5x-10[/tex]
[tex]x^2-5x+18=0[/tex]
Using quadratic formula, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here, a=1 , b=-5 and c=18.
[tex]x=\frac{-(-5)\pm\sqrt{(-5)^2-4(1)(18)}}{2(1)}[/tex]
[tex]x=\frac{5\pm\sqrt{25-72}}{2}[/tex]
[tex]x=\frac{5\pm\sqrt{-47}}{2}[/tex]
[tex]x=\frac{5\pm\sqrt{47}i}{2}[/tex]
