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x^{2}-x-6=6
Use the distributive property to multiply x+2 by x-3 and combine like terms.
x^{2}-x-6-6=0
Subtract 6 from both sides.
x^{2}-x-12=0
Subtract 6 from -6 to get -12.
x=\frac{-\left(-1\right)±\sqrt{1-4\left(-12\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -1 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-1\right)±\sqrt{1+48}}{2}
Multiply -4 times -12.
x=\frac{-\left(-1\right)±\sqrt{49}}{2}
Add 1 to 48.
x=\frac{-\left(-1\right)±7}{2}
Take the square root of 49.
x=\frac{1±7}{2}
The opposite of -1 is 1.
x=\frac{8}{2}
Now solve the equation x=\frac{1±7}{2} when ± is plus. Add 1 to 7.
x=4
Divide 8 by 2.
x=-\frac{6}{2}
Now solve the equation x=\frac{1±7}{2} when ± is minus. Subtract 7 from 1.
x=-3
Divide -6 by 2.
x=4 x=-3
The equation is now solved.
x^{2}-x-6=6
Use the distributive property to multiply x+2 by x-3 and combine like terms.
x^{2}-x=6+6
Add 6 to both sides.
x^{2}-x=12
Add 6 and 6 to get 12.
x^{2}-x+\left(-\frac{1}{2}\right)^{2}=12+\left(-\frac{1}{2}\right)^{2}
Divide -1, the coefficient of the x term, by 2 to get -\frac{1}{2}. Then add the square of -\frac{1}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-x+\frac{1}{4}=12+\frac{1}{4}
Square -\frac{1}{2} by squaring both the numerator and the denominator of the fraction.
x^{2}-x+\frac{1}{4}=\frac{49}{4}
Add 12 to \frac{1}{4}.
\left(x-\frac{1}{2}\right)^{2}=\frac{49}{4}
Factor x^{2}-x+\frac{1}{4}. 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}{2}\right)^{2}}=\sqrt{\frac{49}{4}}
Take the square root of both sides of the equation.
x-\frac{1}{2}=\frac{7}{2} x-\frac{1}{2}=-\frac{7}{2}
Simplify.
x=4 x=-3
Add \frac{1}{2} to both sides of the equation.