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9x^{2}+6x-48=-48
Use the distributive property to multiply 3x-6 by 3x+8 and combine like terms.
9x^{2}+6x-48+48=0
Add 48 to both sides.
9x^{2}+6x=0
Add -48 and 48 to get 0.
x=\frac{-6±\sqrt{6^{2}}}{2\times 9}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 6 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-6±6}{2\times 9}
Take the square root of 6^{2}.
x=\frac{-6±6}{18}
Multiply 2 times 9.
x=\frac{0}{18}
Now solve the equation x=\frac{-6±6}{18} when ± is plus. Add -6 to 6.
x=0
Divide 0 by 18.
x=-\frac{12}{18}
Now solve the equation x=\frac{-6±6}{18} when ± is minus. Subtract 6 from -6.
x=-\frac{2}{3}
Reduce the fraction \frac{-12}{18} to lowest terms by extracting and canceling out 6.
x=0 x=-\frac{2}{3}
The equation is now solved.
9x^{2}+6x-48=-48
Use the distributive property to multiply 3x-6 by 3x+8 and combine like terms.
9x^{2}+6x=-48+48
Add 48 to both sides.
9x^{2}+6x=0
Add -48 and 48 to get 0.
\frac{9x^{2}+6x}{9}=\frac{0}{9}
Divide both sides by 9.
x^{2}+\frac{6}{9}x=\frac{0}{9}
Dividing by 9 undoes the multiplication by 9.
x^{2}+\frac{2}{3}x=\frac{0}{9}
Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.
x^{2}+\frac{2}{3}x=0
Divide 0 by 9.
x^{2}+\frac{2}{3}x+\left(\frac{1}{3}\right)^{2}=\left(\frac{1}{3}\right)^{2}
Divide \frac{2}{3}, the coefficient of the x term, by 2 to get \frac{1}{3}. Then add the square of \frac{1}{3} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+\frac{2}{3}x+\frac{1}{9}=\frac{1}{9}
Square \frac{1}{3} by squaring both the numerator and the denominator of the fraction.
\left(x+\frac{1}{3}\right)^{2}=\frac{1}{9}
Factor x^{2}+\frac{2}{3}x+\frac{1}{9}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x+\frac{1}{3}\right)^{2}}=\sqrt{\frac{1}{9}}
Take the square root of both sides of the equation.
x+\frac{1}{3}=\frac{1}{3} x+\frac{1}{3}=-\frac{1}{3}
Simplify.
x=0 x=-\frac{2}{3}
Subtract \frac{1}{3} from both sides of the equation.