Solve x^2=1-576/49

$${ x }^{ 2 } =1- \frac{ 576 }{ 49 }$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{527}i}{7}\approx -0-3.279497224i$$

$$x=\frac{\sqrt{527}i}{7}\approx 3.279497224i$$

Steps by Finding Square Root

Subtract \frac{576}{49} from 1 to get -\frac{527}{49}.

$$x^{2}=-\frac{527}{49}$$

The equation is now solved.

$$x=\frac{\sqrt{527}i}{7} x=-\frac{\sqrt{527}i}{7}$$

Steps Using the Quadratic Formula

Subtract \frac{576}{49} from 1 to get -\frac{527}{49}.

$$x^{2}=-\frac{527}{49}$$

Add \frac{527}{49} to both sides.

$$x^{2}+\frac{527}{49}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{527}{49} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{527}{49}}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{527}{49}}}{2}$$

Multiply -4 times \frac{527}{49}.

$$x=\frac{0±\sqrt{-\frac{2108}{49}}}{2}$$

Take the square root of -\frac{2108}{49}.

$$x=\frac{0±\frac{2\sqrt{527}i}{7}}{2}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{527}i}{7}}{2} when ± is plus.

$$x=\frac{\sqrt{527}i}{7}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{527}i}{7}}{2} when ± is minus.

$$x=-\frac{\sqrt{527}i}{7}$$

The equation is now solved.

$$x=\frac{\sqrt{527}i}{7} x=-\frac{\sqrt{527}i}{7}$$