Solve 4y^2=448

$$4 y ^ { 2 } = 448$$

Solve for y

$$y=4\sqrt{7}\approx 10.583005244$$

$$y=-4\sqrt{7}\approx -10.583005244$$

Steps by Finding Square Root

Divide both sides by 4.

$$y^{2}=\frac{448}{4}$$

Divide 448 by 4 to get 112.

$$y^{2}=112$$

Take the square root of both sides of the equation.

$$y=4\sqrt{7} y=-4\sqrt{7}$$

Steps Using the Quadratic Formula

Divide both sides by 4.

$$y^{2}=\frac{448}{4}$$

Divide 448 by 4 to get 112.

$$y^{2}=112$$

Subtract 112 from both sides.

$$y^{2}-112=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -112 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-112\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-112\right)}}{2}$$

Multiply -4 times -112.

$$y=\frac{0±\sqrt{448}}{2}$$

Take the square root of 448.

$$y=\frac{0±8\sqrt{7}}{2}$$

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

$$y=4\sqrt{7}$$

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

$$y=-4\sqrt{7}$$

The equation is now solved.

$$y=4\sqrt{7} y=-4\sqrt{7}$$