Solve 4/16+4/4+2/4=x^2

$$\frac{ \frac{ 4 }{ 16 } + \frac{ 4 }{ 4 } +2 }{ 4 } = { x }^{ 2 }$$

Solve for x

$$x=\frac{\sqrt{13}}{4}\approx 0.901387819$$

$$x=-\frac{\sqrt{13}}{4}\approx -0.901387819$$

Steps by Finding Square Root

Multiply both sides of the equation by 4.

$$\frac{4}{16}+\frac{4}{4}+2=4x^{2}$$

Reduce the fraction \frac{4}{16} to lowest terms by extracting and canceling out 4.

$$\frac{1}{4}+\frac{4}{4}+2=4x^{2}$$

Divide 4 by 4 to get 1.

$$\frac{1}{4}+1+2=4x^{2}$$

Add \frac{1}{4} and 1 to get \frac{5}{4}.

$$\frac{5}{4}+2=4x^{2}$$

Add \frac{5}{4} and 2 to get \frac{13}{4}.

$$\frac{13}{4}=4x^{2}$$

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

$$4x^{2}=\frac{13}{4}$$

Divide both sides by 4.

$$x^{2}=\frac{\frac{13}{4}}{4}$$

Express \frac{\frac{13}{4}}{4} as a single fraction.

$$x^{2}=\frac{13}{4\times 4}$$

Multiply 4 and 4 to get 16.

$$x^{2}=\frac{13}{16}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{13}}{4} x=-\frac{\sqrt{13}}{4}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 4.

$$\frac{4}{16}+\frac{4}{4}+2=4x^{2}$$

Reduce the fraction \frac{4}{16} to lowest terms by extracting and canceling out 4.

$$\frac{1}{4}+\frac{4}{4}+2=4x^{2}$$

Divide 4 by 4 to get 1.

$$\frac{1}{4}+1+2=4x^{2}$$

Add \frac{1}{4} and 1 to get \frac{5}{4}.

$$\frac{5}{4}+2=4x^{2}$$

Add \frac{5}{4} and 2 to get \frac{13}{4}.

$$\frac{13}{4}=4x^{2}$$

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

$$4x^{2}=\frac{13}{4}$$

Subtract \frac{13}{4} from both sides.

$$4x^{2}-\frac{13}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -\frac{13}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-\frac{13}{4}\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-\frac{13}{4}\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-\frac{13}{4}\right)}}{2\times 4}$$

Multiply -16 times -\frac{13}{4}.

$$x=\frac{0±\sqrt{52}}{2\times 4}$$

Take the square root of 52.

$$x=\frac{0±2\sqrt{13}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±2\sqrt{13}}{8}$$

Now solve the equation x=\frac{0±2\sqrt{13}}{8} when ± is plus.

$$x=\frac{\sqrt{13}}{4}$$

Now solve the equation x=\frac{0±2\sqrt{13}}{8} when ± is minus.

$$x=-\frac{\sqrt{13}}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{13}}{4} x=-\frac{\sqrt{13}}{4}$$