Answer:
[tex]x=3,x=-1[/tex]
Step-by-step explanation:
Start with:
[tex]x(x-1)-3(x-3)+3(x-2)=x+6[/tex]
Distribute the values on the outside of each of the parentheses.
[tex]x^2-x-3x+9+3x-6=x+6[/tex]
Combine like terms.
[tex]x^2-x+3=x+6[/tex]
Subtract [tex]6[/tex] from both sides of the equation.
[tex]x^2-x-3=x[/tex]
Subtract [tex]x[/tex] from both sides of the equation.
[tex]x^2-2x-3=0[/tex]
Now, we need to use our quadratic equation formula:
[tex]ax^2+bx+c=0[/tex]
[tex]x= \frac{-b+/-\sqrt{b^2-4ac}}{2a}[/tex]
Identify your values.
[tex]a=1\\b=-2\\c=-3[/tex]
Substitute.
(Solve positive)
[tex]x= \frac{-(-2)+\sqrt{(-2)^2-4(1)(-3)}}{2(1)}[/tex]
Solve.
[tex]x= \frac{2+\sqrt{(16}}{2}[/tex]
Find the square root of [tex]16[/tex].
[tex]x=\frac{2+4}{2}[/tex]
Add.
[tex]x=\frac{6}{2}[/tex]
Simplify.
[tex]x=3[/tex]
~
(Solve negative)
[tex]x= \frac{-(-2)-\sqrt{(-2)^2-4(1)(-3)}}{2(1)}[/tex]
Solve.
[tex]x= \frac{2-\sqrt{(16}}{2}[/tex]
Find the square root of [tex]16[/tex].
[tex]x=\frac{2-4}{2}[/tex]
Subtract.
[tex]x=\frac{-2}{2}[/tex]
Simplify.
[tex]x=-1[/tex]
