Solve x^2+52x+6

$${ x }^{ 2 } +52x+6$$

Factor

$$\left(x-\left(-\sqrt{670}-26\right)\right)\left(x-\left(\sqrt{670}-26\right)\right)$$

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.

$$x^{2}+52x+6=0$$

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.

$$x=\frac{-52±\sqrt{52^{2}-4\times 6}}{2}$$

Square 52.

$$x=\frac{-52±\sqrt{2704-4\times 6}}{2}$$

Multiply -4 times 6.

$$x=\frac{-52±\sqrt{2704-24}}{2}$$

Add 2704 to -24.

$$x=\frac{-52±\sqrt{2680}}{2}$$

Take the square root of 2680.

$$x=\frac{-52±2\sqrt{670}}{2}$$

Now solve the equation x=\frac{-52±2\sqrt{670}}{2} when ± is plus. Add -52 to 2\sqrt{670}.

$$x=\frac{2\sqrt{670}-52}{2}$$

Divide -52+2\sqrt{670} by 2.

$$x=\sqrt{670}-26$$

Now solve the equation x=\frac{-52±2\sqrt{670}}{2} when ± is minus. Subtract 2\sqrt{670} from -52.

$$x=\frac{-2\sqrt{670}-52}{2}$$

Divide -52-2\sqrt{670} by 2.

$$x=-\sqrt{670}-26$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -26+\sqrt{670} for x_{1} and -26-\sqrt{670} for x_{2}.

$$x^{2}+52x+6=\left(x-\left(\sqrt{670}-26\right)\right)\left(x-\left(-\sqrt{670}-26\right)\right)$$

Evaluate

$$x^{2}+52x+6$$