Solve 588=4*10*h^2/48

$$588 = \frac { 4 \times 10 \times h ^ { 2 } } { 48 }$$

Solve for h

$$h = \frac{42 \sqrt{10}}{5} \approx 26.563132345$$

$$h = -\frac{42 \sqrt{10}}{5} \approx -26.563132345$$

Steps by Finding Square Root

Multiply both sides by 48.

$$588\times 48=4\times 10h^{2}$$

Multiply 588 and 48 to get 28224.

$$28224=4\times 10h^{2}$$

Multiply 4 and 10 to get 40.

$$28224=40h^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$40h^{2}=28224$$

Divide both sides by 40.

$$h^{2}=\frac{28224}{40}$$

Reduce the fraction \frac{28224}{40} to lowest terms by extracting and canceling out 8.

$$h^{2}=\frac{3528}{5}$$

Take the square root of both sides of the equation.

$$h=\frac{42\sqrt{10}}{5} h=-\frac{42\sqrt{10}}{5}$$

Steps Using the Quadratic Formula

Multiply both sides by 48.

$$588\times 48=4\times 10h^{2}$$

Multiply 588 and 48 to get 28224.

$$28224=4\times 10h^{2}$$

Multiply 4 and 10 to get 40.

$$28224=40h^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$40h^{2}=28224$$

Subtract 28224 from both sides.

$$40h^{2}-28224=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 40 for a, 0 for b, and -28224 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{0±\sqrt{0^{2}-4\times 40\left(-28224\right)}}{2\times 40}$$

Square 0.

$$h=\frac{0±\sqrt{-4\times 40\left(-28224\right)}}{2\times 40}$$

Multiply -4 times 40.

$$h=\frac{0±\sqrt{-160\left(-28224\right)}}{2\times 40}$$

Multiply -160 times -28224.

$$h=\frac{0±\sqrt{4515840}}{2\times 40}$$

Take the square root of 4515840.

$$h=\frac{0±672\sqrt{10}}{2\times 40}$$

Multiply 2 times 40.

$$h=\frac{0±672\sqrt{10}}{80}$$

Now solve the equation h=\frac{0±672\sqrt{10}}{80} when ± is plus.

$$h=\frac{42\sqrt{10}}{5}$$

Now solve the equation h=\frac{0±672\sqrt{10}}{80} when ± is minus.

$$h=-\frac{42\sqrt{10}}{5}$$

The equation is now solved.

$$h=\frac{42\sqrt{10}}{5} h=-\frac{42\sqrt{10}}{5}$$