Solve 416x^2=548

$$416 x ^ { 2 } = 548$$

Solve for x

$$x = \frac{\sqrt{3562}}{52} \approx 1.147740255$$

$$x = -\frac{\sqrt{3562}}{52} \approx -1.147740255$$

Steps by Finding Square Root

Divide both sides by 416.

$$x^{2}=\frac{548}{416}$$

Reduce the fraction \frac{548}{416} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{137}{104}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{3562}}{52} x=-\frac{\sqrt{3562}}{52}$$

Steps Using the Quadratic Formula

Divide both sides by 416.

$$x^{2}=\frac{548}{416}$$

Reduce the fraction \frac{548}{416} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{137}{104}$$

Subtract \frac{137}{104} from both sides.

$$x^{2}-\frac{137}{104}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{137}{104} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{137}{104}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{137}{104}\right)}}{2}$$

Multiply -4 times -\frac{137}{104}.

$$x=\frac{0±\sqrt{\frac{137}{26}}}{2}$$

Take the square root of \frac{137}{26}.

$$x=\frac{0±\frac{\sqrt{3562}}{26}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{3562}}{26}}{2} when ± is plus.

$$x=\frac{\sqrt{3562}}{52}$$

Now solve the equation x=\frac{0±\frac{\sqrt{3562}}{26}}{2} when ± is minus.

$$x=-\frac{\sqrt{3562}}{52}$$

The equation is now solved.

$$x=\frac{\sqrt{3562}}{52} x=-\frac{\sqrt{3562}}{52}$$