Solve x^2+26x-69

$${ x }^{ 2 } +26x-69$$

Factor

$$\left(x-\left(-\sqrt{238}-13\right)\right)\left(x-\left(\sqrt{238}-13\right)\right)$$

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.

$$x^{2}+26x-69=0$$

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.

$$x=\frac{-26±\sqrt{26^{2}-4\left(-69\right)}}{2}$$

Square 26.

$$x=\frac{-26±\sqrt{676-4\left(-69\right)}}{2}$$

Multiply -4 times -69.

$$x=\frac{-26±\sqrt{676+276}}{2}$$

Add 676 to 276.

$$x=\frac{-26±\sqrt{952}}{2}$$

Take the square root of 952.

$$x=\frac{-26±2\sqrt{238}}{2}$$

Now solve the equation x=\frac{-26±2\sqrt{238}}{2} when ± is plus. Add -26 to 2\sqrt{238}.

$$x=\frac{2\sqrt{238}-26}{2}$$

Divide -26+2\sqrt{238} by 2.

$$x=\sqrt{238}-13$$

Now solve the equation x=\frac{-26±2\sqrt{238}}{2} when ± is minus. Subtract 2\sqrt{238} from -26.

$$x=\frac{-2\sqrt{238}-26}{2}$$

Divide -26-2\sqrt{238} by 2.

$$x=-\sqrt{238}-13$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -13+\sqrt{238} for x_{1} and -13-\sqrt{238} for x_{2}.

$$x^{2}+26x-69=\left(x-\left(\sqrt{238}-13\right)\right)\left(x-\left(-\sqrt{238}-13\right)\right)$$

Evaluate

$$x^{2}+26x-69$$