Solve x^2+10x-625

$${ x }^{ 2 } +10x-625$$

Factor

$$\left(x-\left(-5\sqrt{26}-5\right)\right)\left(x-\left(5\sqrt{26}-5\right)\right)$$

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.

$$x^{2}+10x-625=0$$

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.

$$x=\frac{-10±\sqrt{10^{2}-4\left(-625\right)}}{2}$$

Square 10.

$$x=\frac{-10±\sqrt{100-4\left(-625\right)}}{2}$$

Multiply -4 times -625.

$$x=\frac{-10±\sqrt{100+2500}}{2}$$

Add 100 to 2500.

$$x=\frac{-10±\sqrt{2600}}{2}$$

Take the square root of 2600.

$$x=\frac{-10±10\sqrt{26}}{2}$$

Now solve the equation x=\frac{-10±10\sqrt{26}}{2} when ± is plus. Add -10 to 10\sqrt{26}.

$$x=\frac{10\sqrt{26}-10}{2}$$

Divide -10+10\sqrt{26} by 2.

$$x=5\sqrt{26}-5$$

Now solve the equation x=\frac{-10±10\sqrt{26}}{2} when ± is minus. Subtract 10\sqrt{26} from -10.

$$x=\frac{-10\sqrt{26}-10}{2}$$

Divide -10-10\sqrt{26} by 2.

$$x=-5\sqrt{26}-5$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -5+5\sqrt{26} for x_{1} and -5-5\sqrt{26} for x_{2}.

$$x^{2}+10x-625=\left(x-\left(5\sqrt{26}-5\right)\right)\left(x-\left(-5\sqrt{26}-5\right)\right)$$

Evaluate

$$x^{2}+10x-625$$