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Factor
Steps Using the Quadratic Formula
Quadratic polynomial can be factored using the transformation , where and are the solutions of the quadratic equation .
All equations of the form can be solved using the quadratic formula: . The quadratic formula gives two solutions, one when is addition and one when it is subtraction.
Square .
Multiply times .
Multiply times .
Add to .
Take the square root of .
Multiply times .
Now solve the equation when is plus. Add to .
Divide by .
Now solve the equation when is minus. Subtract from .
Divide by .
Factor the original expression using . Substitute for and for .
Evaluate
Graph
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-2x^{2}+8x+4=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{-8±\sqrt{8^{2}-4\left(-2\right)\times 4}}{2\left(-2\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{-8±\sqrt{64-4\left(-2\right)\times 4}}{2\left(-2\right)}
Square 8.
x=\frac{-8±\sqrt{64+8\times 4}}{2\left(-2\right)}
Multiply -4 times -2.
x=\frac{-8±\sqrt{64+32}}{2\left(-2\right)}
Multiply 8 times 4.
x=\frac{-8±\sqrt{96}}{2\left(-2\right)}
Add 64 to 32.
x=\frac{-8±4\sqrt{6}}{2\left(-2\right)}
Take the square root of 96.
x=\frac{-8±4\sqrt{6}}{-4}
Multiply 2 times -2.
x=\frac{4\sqrt{6}-8}{-4}
Now solve the equation x=\frac{-8±4\sqrt{6}}{-4} when ± is plus. Add -8 to 4\sqrt{6}\approx 9.797958971.
x=2-\sqrt{6}
Divide -8+4\sqrt{6}\approx 1.797958971 by -4.
x=\frac{-4\sqrt{6}-8}{-4}
Now solve the equation x=\frac{-8±4\sqrt{6}}{-4} when ± is minus. Subtract 4\sqrt{6}\approx 9.797958971 from -8.
x=\sqrt{6}+2
Divide -8-4\sqrt{6}\approx -17.797958971 by -4.
-2x^{2}+8x+4=-2\left(x-\left(2-\sqrt{6}\right)\right)\left(x-\left(\sqrt{6}+2\right)\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 2-\sqrt{6}\approx -0.449489743 for x_{1} and 2+\sqrt{6}\approx 4.449489743 for x_{2}.
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