Solve 588=4*10*h^2/4.8

$$588 = \frac { 4 \times 10 \times h ^ { 2 } } { 4.8 }$$

Solve for h

$$h=8.4$$

$$h=-8.4$$

Steps by Finding Square Root

Multiply both sides by 4.8.

$$588\times 4.8=4\times 10h^{2}$$

Multiply 588 and 4.8 to get 2822.4.

$$2822.4=4\times 10h^{2}$$

Multiply 4 and 10 to get 40.

$$2822.4=40h^{2}$$

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

$$40h^{2}=2822.4$$

Divide both sides by 40.

$$h^{2}=\frac{2822.4}{40}$$

Expand \frac{2822.4}{40} by multiplying both numerator and the denominator by 10.

$$h^{2}=\frac{28224}{400}$$

Reduce the fraction \frac{28224}{400} to lowest terms by extracting and canceling out 16.

$$h^{2}=\frac{1764}{25}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Multiply both sides by 4.8.

$$588\times 4.8=4\times 10h^{2}$$

Multiply 588 and 4.8 to get 2822.4.

$$2822.4=4\times 10h^{2}$$

Multiply 4 and 10 to get 40.

$$2822.4=40h^{2}$$

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

$$40h^{2}=2822.4$$

Subtract 2822.4 from both sides.

$$40h^{2}-2822.4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 40 for a, 0 for b, and -2822.4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{0±\sqrt{0^{2}-4\times 40\left(-2822.4\right)}}{2\times 40}$$

Square 0.

$$h=\frac{0±\sqrt{-4\times 40\left(-2822.4\right)}}{2\times 40}$$

Multiply -4 times 40.

$$h=\frac{0±\sqrt{-160\left(-2822.4\right)}}{2\times 40}$$

Multiply -160 times -2822.4.

$$h=\frac{0±\sqrt{451584}}{2\times 40}$$

Take the square root of 451584.

$$h=\frac{0±672}{2\times 40}$$

Multiply 2 times 40.

$$h=\frac{0±672}{80}$$

Now solve the equation h=\frac{0±672}{80} when ± is plus. Reduce the fraction \frac{672}{80} to lowest terms by extracting and canceling out 16.

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

Now solve the equation h=\frac{0±672}{80} when ± is minus. Reduce the fraction \frac{-672}{80} to lowest terms by extracting and canceling out 16.

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

The equation is now solved.

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