Solve x^2=48/49

$${ x }^{ 2 } = \frac{ 48 }{ 49 }$$

Solve for x

$$x=\frac{4\sqrt{3}}{7}\approx 0.989743319$$

$$x=-\frac{4\sqrt{3}}{7}\approx -0.989743319$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{3}}{7} x=-\frac{4\sqrt{3}}{7}$$

Steps Using the Quadratic Formula

Subtract \frac{48}{49} from both sides.

$$x^{2}-\frac{48}{49}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{48}{49} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{48}{49}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{48}{49}\right)}}{2}$$

Multiply -4 times -\frac{48}{49}.

$$x=\frac{0±\sqrt{\frac{192}{49}}}{2}$$

Take the square root of \frac{192}{49}.

$$x=\frac{0±\frac{8\sqrt{3}}{7}}{2}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{3}}{7}}{2} when ± is plus.

$$x=\frac{4\sqrt{3}}{7}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{3}}{7}}{2} when ± is minus.

$$x=-\frac{4\sqrt{3}}{7}$$

The equation is now solved.

$$x=\frac{4\sqrt{3}}{7} x=-\frac{4\sqrt{3}}{7}$$