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0-x^{2}+9x-9
Anything times zero gives zero.
-9-x^{2}+9x
Subtract 9 from 0 to get -9.
factor(0-x^{2}+9x-9)
Anything times zero gives zero.
factor(-9-x^{2}+9x)
Subtract 9 from 0 to get -9.
-x^{2}+9x-9=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
x=\frac{-9±\sqrt{9^{2}-4\left(-1\right)\left(-9\right)}}{2\left(-1\right)}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-9±\sqrt{81-4\left(-1\right)\left(-9\right)}}{2\left(-1\right)}
Square 9.
x=\frac{-9±\sqrt{81+4\left(-9\right)}}{2\left(-1\right)}
Multiply -4 times -1.
x=\frac{-9±\sqrt{81-36}}{2\left(-1\right)}
Multiply 4 times -9.
x=\frac{-9±\sqrt{45}}{2\left(-1\right)}
Add 81 to -36.
x=\frac{-9±3\sqrt{5}}{2\left(-1\right)}
Take the square root of 45.
x=\frac{-9±3\sqrt{5}}{-2}
Multiply 2 times -1.
x=\frac{3\sqrt{5}-9}{-2}
Now solve the equation x=\frac{-9±3\sqrt{5}}{-2} when ± is plus. Add -9 to 3\sqrt{5}.
x=\frac{9-3\sqrt{5}}{2}
Divide -9+3\sqrt{5} by -2.
x=\frac{-3\sqrt{5}-9}{-2}
Now solve the equation x=\frac{-9±3\sqrt{5}}{-2} when ± is minus. Subtract 3\sqrt{5} from -9.
x=\frac{3\sqrt{5}+9}{2}
Divide -9-3\sqrt{5} by -2.
-x^{2}+9x-9=-\left(x-\frac{9-3\sqrt{5}}{2}\right)\left(x-\frac{3\sqrt{5}+9}{2}\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{9-3\sqrt{5}}{2} for x_{1} and \frac{9+3\sqrt{5}}{2} for x_{2}.