Respuesta :
Answer: x= [tex]x=-\frac{-7+\sqrt{73}}{4},\:x=\frac{7+\sqrt{73}}{4}[/tex]
Steps:
[tex]-3\left(x+3\right)=-6\left(x-3\right)x[/tex]
− 3(x + 3 ): − 3x − 9
− 6(x − 3 )x: − 6x + 18x
[tex]-3x-9=-6x^2+18x[/tex]
[tex]Switch\:sides[/tex]
[tex]-6x^2+18x=-3x-9[/tex]
[tex]\mathrm{Add\:}9\mathrm{\:to\:both\:sides}[/tex]
[tex]-6x^2+18x+9=-3x-9+9[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]-6x^2+18x+9=-3x[/tex]
[tex]\mathrm{Add\:}3x\mathrm{\:to\:both\:sides}[/tex]
[tex]-6x^2+18x+9+3x=-3x+3x[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]-6x^2+21x+9=0[/tex]
Solve with the quadratic formula
[tex]x_{1,\:2}=\frac{-21\pm \sqrt{21^2-4\left(-6\right)\cdot \:9}}{2\left(-6\right)}[/tex]
[tex]-3(x+3) =-6 (x-3)x -[/tex]
[tex]x_{1,\:2}=\frac{-21\pm \:3\sqrt{73}}{2\left(-6\right)}[/tex]
[tex]\mathrm{Separate\:the\:solutions}[/tex]
[tex]x_1=\frac{-21+3\sqrt{73}}{2\left(-6\right)},\:x_2=\frac{-21-3\sqrt{73}}{2\left(-6\right)}[/tex]
[tex]-\frac{\sqrt{73}-7}{4}[/tex]
[tex]x =2 −6−21 − 3 73:4√ 7 + 73[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]
[tex]x=-\frac{-7+\sqrt{73}}{4},\:x=\frac{7+\sqrt{73}}{4}[/tex]
Hope This Helps!
