Question

-3(x + 3) = -6 (x - 3) x= ?

Answer 1

Answer: x= $x=-\frac{-7+\sqrt{73}}{4},\:x=\frac{7+\sqrt{73}}{4}$

Steps:

$-3\left(x+3\right)=-6\left(x-3\right)x$

− 3(x + 3 ): − 3x − 9

− 6(x − 3 )x: − 6x + 18x

$-3x-9=-6x^2+18x$

$Switch\:sides$

$-6x^2+18x=-3x-9$

$\mathrm{Add\:}9\mathrm{\:to\:both\:sides}$

$-6x^2+18x+9=-3x-9+9$

$\mathrm{Simplify}$

$-6x^2+18x+9=-3x$

$\mathrm{Add\:}3x\mathrm{\:to\:both\:sides}$

$-6x^2+18x+9+3x=-3x+3x$

$\mathrm{Simplify}$

$-6x^2+21x+9=0$

Solve with the quadratic formula

$x_{1,\:2}=\frac{-21\pm \sqrt{21^2-4\left(-6\right)\cdot \:9}}{2\left(-6\right)}$

$-3(x+3) =-6 (x-3)x -$

$x_{1,\:2}=\frac{-21\pm \:3\sqrt{73}}{2\left(-6\right)}$

$\mathrm{Separate\:the\:solutions}$

$x_1=\frac{-21+3\sqrt{73}}{2\left(-6\right)},\:x_2=\frac{-21-3\sqrt{73}}{2\left(-6\right)}$

$-\frac{\sqrt{73}-7}{4}$

$x =2 −6−21 − 3 73:4√ 7 + 73$

$\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}$

$x=-\frac{-7+\sqrt{73}}{4},\:x=\frac{7+\sqrt{73}}{4}$

Hope This Helps!