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

$$( 4 x ) ^ { 2 } + 2 ^ { 2 } = x ^ { 2 }$$

Solve for x (complex solution)

$$x=-\frac{2\sqrt{15}i}{15}\approx -0-0.516397779i$$

$$x=\frac{2\sqrt{15}i}{15}\approx 0.516397779i$$

Steps by Finding Square Root

Expand \left(4x\right)^{2}.

$$4^{2}x^{2}+2^{2}=x^{2}$$

Calculate 4 to the power of 2 and get 16.

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

Calculate 2 to the power of 2 and get 4.

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

Subtract x^{2} from both sides.

$$16x^{2}+4-x^{2}=0$$

Combine 16x^{2} and -x^{2} to get 15x^{2}.

$$15x^{2}+4=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$15x^{2}=-4$$

Divide both sides by 15.

$$x^{2}=-\frac{4}{15}$$

The equation is now solved.

$$x=\frac{2\sqrt{15}i}{15} x=-\frac{2\sqrt{15}i}{15}$$

Steps Using the Quadratic Formula

Expand \left(4x\right)^{2}.

$$4^{2}x^{2}+2^{2}=x^{2}$$

Calculate 4 to the power of 2 and get 16.

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

Calculate 2 to the power of 2 and get 4.

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

Subtract x^{2} from both sides.

$$16x^{2}+4-x^{2}=0$$

Combine 16x^{2} and -x^{2} to get 15x^{2}.

$$15x^{2}+4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 15 for a, 0 for b, and 4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 15\times 4}}{2\times 15}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 15\times 4}}{2\times 15}$$

Multiply -4 times 15.

$$x=\frac{0±\sqrt{-60\times 4}}{2\times 15}$$

Multiply -60 times 4.

$$x=\frac{0±\sqrt{-240}}{2\times 15}$$

Take the square root of -240.

$$x=\frac{0±4\sqrt{15}i}{2\times 15}$$

Multiply 2 times 15.

$$x=\frac{0±4\sqrt{15}i}{30}$$

Now solve the equation x=\frac{0±4\sqrt{15}i}{30} when ± is plus.

$$x=\frac{2\sqrt{15}i}{15}$$

Now solve the equation x=\frac{0±4\sqrt{15}i}{30} when ± is minus.

$$x=-\frac{2\sqrt{15}i}{15}$$

The equation is now solved.

$$x=\frac{2\sqrt{15}i}{15} x=-\frac{2\sqrt{15}i}{15}$$