Question

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

Answer 1

Answer:

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

Answer 2

Answer:

The solutions of $x^{2}=8-5 x$ are  $\frac{-5+\sqrt{57}}{2} \text { and } \frac{-5-\sqrt{57}}{2}$

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, $x=\frac{-5+\sqrt{5^{2}-4 \times 1 \times(-8)}}{2 \times 1}$

$=\frac{-5+\sqrt{25-(-32)}}{2}=\frac{-5+\sqrt{25+32}}{2}=\frac{-5+\sqrt{57}}{2}$

Again $x=\frac{-5-\sqrt{57}}{2}$

So the solution of $x=\frac{-5+\sqrt{57}}{2} \text { and } \frac{-5-\sqrt{57}}{2}$