Solve 1330=16x^2

$$1330=16 { x }^{ 2 }$$

Solve for x

$$x = \frac{\sqrt{1330}}{4} \approx 9.117291264$$

$$x = -\frac{\sqrt{1330}}{4} \approx -9.117291264$$

Steps by Finding Square Root

Divide both sides by 16.

$$\frac{1330}{16}=x^{2}$$

Reduce the fraction \frac{1330}{16} to lowest terms by extracting and canceling out 2.

$$\frac{665}{8}=x^{2}$$

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

$$x^{2}=\frac{665}{8}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{1330}}{4} x=-\frac{\sqrt{1330}}{4}$$

Steps Using the Quadratic Formula

Divide both sides by 16.

$$\frac{1330}{16}=x^{2}$$

Reduce the fraction \frac{1330}{16} to lowest terms by extracting and canceling out 2.

$$\frac{665}{8}=x^{2}$$

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

$$x^{2}=\frac{665}{8}$$

Subtract \frac{665}{8} from both sides.

$$x^{2}-\frac{665}{8}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{665}{8} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{665}{8}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{665}{8}\right)}}{2}$$

Multiply -4 times -\frac{665}{8}.

$$x=\frac{0±\sqrt{\frac{665}{2}}}{2}$$

Take the square root of \frac{665}{2}.

$$x=\frac{0±\frac{\sqrt{1330}}{2}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{1330}}{2}}{2} when ± is plus.

$$x=\frac{\sqrt{1330}}{4}$$

Now solve the equation x=\frac{0±\frac{\sqrt{1330}}{2}}{2} when ± is minus.

$$x=-\frac{\sqrt{1330}}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{1330}}{4} x=-\frac{\sqrt{1330}}{4}$$