Solve 56y^2-182=0

$$56 y ^ { 2 } - 182 = 0$$

Solve for y

$$y = \frac{\sqrt{13}}{2} \approx 1.802775638$$

$$y = -\frac{\sqrt{13}}{2} \approx -1.802775638$$

Steps by Finding Square Root

Add 182 to both sides. Anything plus zero gives itself.

$$56y^{2}=182$$

Divide both sides by 56.

$$y^{2}=\frac{182}{56}$$

Reduce the fraction \frac{182}{56} to lowest terms by extracting and canceling out 14.

$$y^{2}=\frac{13}{4}$$

Take the square root of both sides of the equation.

$$y=\frac{\sqrt{13}}{2} y=-\frac{\sqrt{13}}{2}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$56y^{2}-182=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 56 for a, 0 for b, and -182 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 56\left(-182\right)}}{2\times 56}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 56\left(-182\right)}}{2\times 56}$$

Multiply -4 times 56.

$$y=\frac{0±\sqrt{-224\left(-182\right)}}{2\times 56}$$

Multiply -224 times -182.

$$y=\frac{0±\sqrt{40768}}{2\times 56}$$

Take the square root of 40768.

$$y=\frac{0±56\sqrt{13}}{2\times 56}$$

Multiply 2 times 56.

$$y=\frac{0±56\sqrt{13}}{112}$$

Now solve the equation y=\frac{0±56\sqrt{13}}{112} when ± is plus.

$$y=\frac{\sqrt{13}}{2}$$

Now solve the equation y=\frac{0±56\sqrt{13}}{112} when ± is minus.

$$y=-\frac{\sqrt{13}}{2}$$

The equation is now solved.

$$y=\frac{\sqrt{13}}{2} y=-\frac{\sqrt{13}}{2}$$