# How do you solve x^2=x+6?

Feb 4, 2016

${x}^{2} = x + 6$

$\rightarrow {x}^{2} - x = 6$

$\rightarrow {x}^{2} - x - 6 = 0$

Now this is a Quadratic equation (in form $a {x}^{2} + b {x}^{2} + c$)

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

In this case $a = 1 , b = - 1 , c = - 6$

$\rightarrow x = \frac{- \left(- 1\right) \pm \sqrt{{\left(- 1\right)}^{2} - 4 \left(1\right) \left(- 6\right)}}{2 \left(1\right)}$

$\rightarrow x = \frac{1 \pm \sqrt{1 - \left(- 24\right)}}{2}$

$\rightarrow x = \frac{1 \pm \sqrt{1 + 24}}{2}$

$\rightarrow x = \frac{1 \pm \sqrt{25}}{2}$

$\rightarrow x = \frac{1 \pm 5}{2}$

Now we are in a stage in which we take the two answers:

$\rightarrow x = \frac{1 + 5}{2} , \frac{1 - 5}{2}$

$\rightarrow x = \frac{6}{2} , - \frac{4}{2}$

$\rightarrow x = 3 , - 2$

Feb 4, 2016

This is another way of solving this equation:

${x}^{2} = x + 6$

$\rightarrow {x}^{2} - x - 6 = 0$

Factor:

$\rightarrow \left(x - 3\right) \left(x + 2\right) = 0$

$\rightarrow x = 3 , - 2$

=)