Question

What are the solutions of x2 = 8 – 5x?

Answer 1

`x - 5 = 8 \\ x = 13 \\ and \: x = 8 \\ so \: you \: have \: two \: solutions`

Answer 2

The solutions of
`x^(2)=8-5 x` are
`(-5+√(57))/(2) \text { and } (-5-√(57))/(2)`

Solution:

The equation is

`x^(2)=8-5 x`

`\Rightarrow x^(2)+5 x-8=0`

We know that the quadratic formula to solve this,

x has two values which are
`= \frac{(-b+\sqrt{b^(2)-4 a c})}{2 a} \text { and } \frac{(-b-\sqrt{\left.b^(2)-4 a c\right)}}{2 a}`

Here a =1, b=5, c =-8

Substituting the values we get,

So,
`x=\frac{-5+\sqrt{5^(2)-4 * 1 *(-8)}}{2 * 1}`

`=(-5+√(25-(-32)))/(2)=(-5+√(25+32))/(2)=(-5+√(57))/(2)`

Again
`x=(-5-√(57))/(2)`

So the solution of
`x=(-5+√(57))/(2) \text { and } (-5-√(57))/(2)`