Solve x^2+527x++665

$${ x }^{ 2 } +527x++665$$

Factor

$$\left(x-\frac{-\sqrt{275069}-527}{2}\right)\left(x-\frac{\sqrt{275069}-527}{2}\right)$$

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.

$$x^{2}+527x+665=0$$

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.

$$x=\frac{-527±\sqrt{527^{2}-4\times 665}}{2}$$

Square 527.

$$x=\frac{-527±\sqrt{277729-4\times 665}}{2}$$

Multiply -4 times 665.

$$x=\frac{-527±\sqrt{277729-2660}}{2}$$

Add 277729 to -2660.

$$x=\frac{-527±\sqrt{275069}}{2}$$

Now solve the equation x=\frac{-527±\sqrt{275069}}{2} when ± is plus. Add -527 to \sqrt{275069}.

$$x=\frac{\sqrt{275069}-527}{2}$$

Now solve the equation x=\frac{-527±\sqrt{275069}}{2} when ± is minus. Subtract \sqrt{275069} from -527.

$$x=\frac{-\sqrt{275069}-527}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-527+\sqrt{275069}}{2} for x_{1} and \frac{-527-\sqrt{275069}}{2} for x_{2}.

$$x^{2}+527x+665=\left(x-\frac{\sqrt{275069}-527}{2}\right)\left(x-\frac{-\sqrt{275069}-527}{2}\right)$$

Evaluate

$$x^{2}+527x+665$$