Solve x^2+82x+26

$${ x }^{ 2 } +82x+26$$

Factor

$$\left(x-\left(-\sqrt{1655}-41\right)\right)\left(x-\left(\sqrt{1655}-41\right)\right)$$

Steps Using the Quadratic Formula

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.

$$x^{2}+82x+26=0$$

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.

$$x=\frac{-82±\sqrt{82^{2}-4\times 26}}{2}$$

Square 82.

$$x=\frac{-82±\sqrt{6724-4\times 26}}{2}$$

Multiply -4 times 26.

$$x=\frac{-82±\sqrt{6724-104}}{2}$$

Add 6724 to -104.

$$x=\frac{-82±\sqrt{6620}}{2}$$

Take the square root of 6620.

$$x=\frac{-82±2\sqrt{1655}}{2}$$

Now solve the equation x=\frac{-82±2\sqrt{1655}}{2} when ± is plus. Add -82 to 2\sqrt{1655}.

$$x=\frac{2\sqrt{1655}-82}{2}$$

Divide -82+2\sqrt{1655} by 2.

$$x=\sqrt{1655}-41$$

Now solve the equation x=\frac{-82±2\sqrt{1655}}{2} when ± is minus. Subtract 2\sqrt{1655} from -82.

$$x=\frac{-2\sqrt{1655}-82}{2}$$

Divide -82-2\sqrt{1655} by 2.

$$x=-\sqrt{1655}-41$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -41+\sqrt{1655} for x_{1} and -41-\sqrt{1655} for x_{2}.

$$x^{2}+82x+26=\left(x-\left(\sqrt{1655}-41\right)\right)\left(x-\left(-\sqrt{1655}-41\right)\right)$$

Evaluate

$$x^{2}+82x+26$$