Solve 195/360x^2=175.5

$$\frac{ 195 }{ 360 } { x }^{ 2 } = 175.5$$

Solve for x

$$x=18$$

$$x=-18$$

Steps by Finding Square Root

Reduce the fraction \frac{195}{360} to lowest terms by extracting and canceling out 15.

$$\frac{13}{24}x^{2}=175.5$$

Multiply both sides by \frac{24}{13}, the reciprocal of \frac{13}{24}.

$$x^{2}=175.5\times \frac{24}{13}$$

Multiply 175.5 and \frac{24}{13} to get 324.

$$x^{2}=324$$

Take the square root of both sides of the equation.

$$x=18 x=-18$$

Steps Using the Quadratic Formula

Reduce the fraction \frac{195}{360} to lowest terms by extracting and canceling out 15.

$$\frac{13}{24}x^{2}=175.5$$

Subtract 175.5 from both sides.

$$\frac{13}{24}x^{2}-175.5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{13}{24} for a, 0 for b, and -175.5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{13}{24}\left(-175.5\right)}}{2\times \frac{13}{24}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{13}{24}\left(-175.5\right)}}{2\times \frac{13}{24}}$$

Multiply -4 times \frac{13}{24}.

$$x=\frac{0±\sqrt{-\frac{13}{6}\left(-175.5\right)}}{2\times \frac{13}{24}}$$

Multiply -\frac{13}{6} times -175.5 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{\frac{1521}{4}}}{2\times \frac{13}{24}}$$

Take the square root of \frac{1521}{4}.

$$x=\frac{0±\frac{39}{2}}{2\times \frac{13}{24}}$$

Multiply 2 times \frac{13}{24}.

$$x=\frac{0±\frac{39}{2}}{\frac{13}{12}}$$

Now solve the equation x=\frac{0±\frac{39}{2}}{\frac{13}{12}} when ± is plus.

$$x=18$$

Now solve the equation x=\frac{0±\frac{39}{2}}{\frac{13}{12}} when ± is minus.

$$x=-18$$

The equation is now solved.

$$x=18 x=-18$$