Solve 0=x^2+16x-112.6*16

$$0 = x ^ { 2 } + 16 x - 112.6 \times 16$$

Solve for x

$$x=\frac{4\sqrt{2915}}{5}-8\approx 35.192591957$$

$$x=-\frac{4\sqrt{2915}}{5}-8\approx -51.192591957$$

Steps Using the Quadratic Formula

Multiply 112.6 and 16 to get 1801.6.

$$0=x^{2}+16x-1801.6$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+16x-1801.6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 16 for b, and -1801.6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-16±\sqrt{16^{2}-4\left(-1801.6\right)}}{2}$$

Square 16.

$$x=\frac{-16±\sqrt{256-4\left(-1801.6\right)}}{2}$$

Multiply -4 times -1801.6.

$$x=\frac{-16±\sqrt{256+7206.4}}{2}$$

Add 256 to 7206.4.

$$x=\frac{-16±\sqrt{7462.4}}{2}$$

Take the square root of 7462.4.

$$x=\frac{-16±\frac{8\sqrt{2915}}{5}}{2}$$

Now solve the equation x=\frac{-16±\frac{8\sqrt{2915}}{5}}{2} when ± is plus. Add -16 to \frac{8\sqrt{2915}}{5}.

$$x=\frac{\frac{8\sqrt{2915}}{5}-16}{2}$$

Divide -16+\frac{8\sqrt{2915}}{5} by 2.

$$x=\frac{4\sqrt{2915}}{5}-8$$

Now solve the equation x=\frac{-16±\frac{8\sqrt{2915}}{5}}{2} when ± is minus. Subtract \frac{8\sqrt{2915}}{5} from -16.

$$x=\frac{-\frac{8\sqrt{2915}}{5}-16}{2}$$

Divide -16-\frac{8\sqrt{2915}}{5} by 2.

$$x=-\frac{4\sqrt{2915}}{5}-8$$

The equation is now solved.

$$x=\frac{4\sqrt{2915}}{5}-8 x=-\frac{4\sqrt{2915}}{5}-8$$

Steps for Completing the Square

Multiply 112.6 and 16 to get 1801.6.

$$0=x^{2}+16x-1801.6$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+16x-1801.6=0$$

Add 1801.6 to both sides. Anything plus zero gives itself.

$$x^{2}+16x=1801.6$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$x^{2}+16x=\frac{9008}{5}$$

Divide 16, the coefficient of the x term, by 2 to get 8. Then add the square of 8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+16x+8^{2}=\frac{9008}{5}+8^{2}$$

Square 8.

$$x^{2}+16x+64=\frac{9008}{5}+64$$

Add \frac{9008}{5} to 64.

$$x^{2}+16x+64=\frac{9328}{5}$$

Factor x^{2}+16x+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+8\right)^{2}=\frac{9328}{5}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+8\right)^{2}}=\sqrt{\frac{9328}{5}}$$

Simplify.

$$x+8=\frac{4\sqrt{2915}}{5} x+8=-\frac{4\sqrt{2915}}{5}$$

Subtract 8 from both sides of the equation.

$$x=\frac{4\sqrt{2915}}{5}-8 x=-\frac{4\sqrt{2915}}{5}-8$$