Solve (2x)^2+x^2=3/4x^2

$$( 2 x ) ^ { 2 } + x ^ { 2 } = \frac { 3 } { 4 } x ^ { 2 }$$

Solve for x

$$x=0$$

Steps by Finding Square Root

Expand \left(2x\right)^{2}.

$$2^{2}x^{2}+x^{2}=\frac{3}{4}x^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}+x^{2}=\frac{3}{4}x^{2}$$

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$5x^{2}=\frac{3}{4}x^{2}$$

Subtract \frac{3}{4}x^{2} from both sides.

$$5x^{2}-\frac{3}{4}x^{2}=0$$

Combine 5x^{2} and -\frac{3}{4}x^{2} to get \frac{17}{4}x^{2}.

$$\frac{17}{4}x^{2}=0$$

Multiply both sides by \frac{4}{17}, the reciprocal of \frac{17}{4}. Anything times zero gives zero.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

Expand \left(2x\right)^{2}.

$$2^{2}x^{2}+x^{2}=\frac{3}{4}x^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}+x^{2}=\frac{3}{4}x^{2}$$

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$5x^{2}=\frac{3}{4}x^{2}$$

Subtract \frac{3}{4}x^{2} from both sides.

$$5x^{2}-\frac{3}{4}x^{2}=0$$

Combine 5x^{2} and -\frac{3}{4}x^{2} to get \frac{17}{4}x^{2}.

$$\frac{17}{4}x^{2}=0$$

Multiply both sides by \frac{4}{17}, the reciprocal of \frac{17}{4}. Anything times zero gives zero.

$$x^{2}=0$$

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

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2}$$

Divide 0 by 2.

$$x=0$$