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y^{2}+8y+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.
y=\frac{-8±\sqrt{8^{2}-4\times 4}}{2}
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.
y=\frac{-8±\sqrt{64-4\times 4}}{2}
Square 8.
y=\frac{-8±\sqrt{64-16}}{2}
Multiply -4 times 4.
y=\frac{-8±\sqrt{48}}{2}
Add 64 to -16.
y=\frac{-8±4\sqrt{3}}{2}
Take the square root of 48.
y=\frac{4\sqrt{3}-8}{2}
Now solve the equation y=\frac{-8±4\sqrt{3}}{2} when ± is plus. Add -8 to 4\sqrt{3}.
y=2\sqrt{3}-4
Divide -8+4\sqrt{3} by 2.
y=\frac{-4\sqrt{3}-8}{2}
Now solve the equation y=\frac{-8±4\sqrt{3}}{2} when ± is minus. Subtract 4\sqrt{3} from -8.
y=-2\sqrt{3}-4
Divide -8-4\sqrt{3} by 2.
y^{2}+8y+4=\left(y-\left(2\sqrt{3}-4\right)\right)\left(y-\left(-2\sqrt{3}-4\right)\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -4+2\sqrt{3} for x_{1} and -4-2\sqrt{3} for x_{2}.