Solve (x^2+16x+16)-25

$$( { x }^{ 2 } +16x+16)-25$$

Factor

$$\left(x-\left(-\sqrt{73}-8\right)\right)\left(x-\left(\sqrt{73}-8\right)\right)$$

Steps Using the Quadratic Formula

Subtract 25 from 16 to get -9.

$$factor(x^{2}+16x-9)$$

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.

$$x^{2}+16x-9=0$$

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.

$$x=\frac{-16±\sqrt{16^{2}-4\left(-9\right)}}{2}$$

Square 16.

$$x=\frac{-16±\sqrt{256-4\left(-9\right)}}{2}$$

Multiply -4 times -9.

$$x=\frac{-16±\sqrt{256+36}}{2}$$

Add 256 to 36.

$$x=\frac{-16±\sqrt{292}}{2}$$

Take the square root of 292.

$$x=\frac{-16±2\sqrt{73}}{2}$$

Now solve the equation x=\frac{-16±2\sqrt{73}}{2} when ± is plus. Add -16 to 2\sqrt{73}.

$$x=\frac{2\sqrt{73}-16}{2}$$

Divide -16+2\sqrt{73} by 2.

$$x=\sqrt{73}-8$$

Now solve the equation x=\frac{-16±2\sqrt{73}}{2} when ± is minus. Subtract 2\sqrt{73} from -16.

$$x=\frac{-2\sqrt{73}-16}{2}$$

Divide -16-2\sqrt{73} by 2.

$$x=-\sqrt{73}-8$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -8+\sqrt{73} for x_{1} and -8-\sqrt{73} for x_{2}.

$$x^{2}+16x-9=\left(x-\left(\sqrt{73}-8\right)\right)\left(x-\left(-\sqrt{73}-8\right)\right)$$

Evaluate

$$x^{2}+16x-9$$

Solution Steps

Subtract 25 from 16 to get -9.

$$x^{2}+16x-9$$