Solve 9.8*0.054=0.5x^2

$$9.8 \times 0.054 = 0.5 x ^ { 2 }$$

Solve for x

$$x = \frac{21 \sqrt{6}}{50} \approx 1.028785692$$

$$x = -\frac{21 \sqrt{6}}{50} \approx -1.028785692$$

Steps by Finding Square Root

Multiply 9.8 and 0.054 to get 0.5292.

$$0.5292=0.5x^{2}$$

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

$$0.5x^{2}=0.5292$$

Divide both sides by 0.5.

$$x^{2}=\frac{0.5292}{0.5}$$

Expand \frac{0.5292}{0.5} by multiplying both numerator and the denominator by 10000.

$$x^{2}=\frac{5292}{5000}$$

Reduce the fraction \frac{5292}{5000} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{1323}{1250}$$

Take the square root of both sides of the equation.

$$x=\frac{21\sqrt{6}}{50} x=-\frac{21\sqrt{6}}{50}$$

Steps Using the Quadratic Formula

Multiply 9.8 and 0.054 to get 0.5292.

$$0.5292=0.5x^{2}$$

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

$$0.5x^{2}=0.5292$$

Subtract 0.5292 from both sides.

$$0.5x^{2}-0.5292=0$$

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.

$$\frac{1}{2}x^{2}-0.5292=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{2} for a, 0 for b, and -0.5292 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{2}\left(-0.5292\right)}}{2\times \frac{1}{2}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{2}\left(-0.5292\right)}}{2\times \frac{1}{2}}$$

Multiply -4 times \frac{1}{2}.

$$x=\frac{0±\sqrt{-2\left(-0.5292\right)}}{2\times \frac{1}{2}}$$

Multiply -2 times -0.5292.

$$x=\frac{0±\sqrt{1.0584}}{2\times \frac{1}{2}}$$

Take the square root of 1.0584.

$$x=\frac{0±\frac{21\sqrt{6}}{50}}{2\times \frac{1}{2}}$$

Multiply 2 times \frac{1}{2}.

$$x=\frac{0±\frac{21\sqrt{6}}{50}}{1}$$

Now solve the equation x=\frac{0±\frac{21\sqrt{6}}{50}}{1} when ± is plus.

$$x=\frac{21\sqrt{6}}{50}$$

Now solve the equation x=\frac{0±\frac{21\sqrt{6}}{50}}{1} when ± is minus.

$$x=-\frac{21\sqrt{6}}{50}$$

The equation is now solved.

$$x=\frac{21\sqrt{6}}{50} x=-\frac{21\sqrt{6}}{50}$$