Solve 2x^2+25x+26

$$2 { x }^{ 2 } +25x+26$$

Factor

$$2\left(x-\frac{-\sqrt{417}-25}{4}\right)\left(x-\frac{\sqrt{417}-25}{4}\right)$$

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.

$$2x^{2}+25x+26=0$$

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.

$$x=\frac{-25±\sqrt{25^{2}-4\times 2\times 26}}{2\times 2}$$

Square 25.

$$x=\frac{-25±\sqrt{625-4\times 2\times 26}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-25±\sqrt{625-8\times 26}}{2\times 2}$$

Multiply -8 times 26.

$$x=\frac{-25±\sqrt{625-208}}{2\times 2}$$

Add 625 to -208.

$$x=\frac{-25±\sqrt{417}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-25±\sqrt{417}}{4}$$

Now solve the equation x=\frac{-25±\sqrt{417}}{4} when ± is plus. Add -25 to \sqrt{417}.

$$x=\frac{\sqrt{417}-25}{4}$$

Now solve the equation x=\frac{-25±\sqrt{417}}{4} when ± is minus. Subtract \sqrt{417} from -25.

$$x=\frac{-\sqrt{417}-25}{4}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-25+\sqrt{417}}{4} for x_{1} and \frac{-25-\sqrt{417}}{4} for x_{2}.

$$2x^{2}+25x+26=2\left(x-\frac{\sqrt{417}-25}{4}\right)\left(x-\frac{-\sqrt{417}-25}{4}\right)$$

Evaluate

$$2x^{2}+25x+26$$