Solve 3.2288=1/20.879x^2

$$3.2288 = \frac { 1 } { 2 } 0.879 x ^ { 2 }$$

Solve for x

$$x = \frac{4 \sqrt{8869110}}{4395} \approx 2.71044833$$

$$x = -\frac{4 \sqrt{8869110}}{4395} \approx -2.71044833$$

Steps by Finding Square Root

Multiply \frac{1}{2} and 0.879 to get \frac{879}{2000}.

$$3.2288=\frac{879}{2000}x^{2}$$

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

$$\frac{879}{2000}x^{2}=3.2288$$

Multiply both sides by \frac{2000}{879}, the reciprocal of \frac{879}{2000}.

$$x^{2}=3.2288\times \frac{2000}{879}$$

Multiply 3.2288 and \frac{2000}{879} to get \frac{32288}{4395}.

$$x^{2}=\frac{32288}{4395}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{8869110}}{4395} x=-\frac{4\sqrt{8869110}}{4395}$$

Steps Using the Quadratic Formula

Multiply \frac{1}{2} and 0.879 to get \frac{879}{2000}.

$$3.2288=\frac{879}{2000}x^{2}$$

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

$$\frac{879}{2000}x^{2}=3.2288$$

Subtract 3.2288 from both sides.

$$\frac{879}{2000}x^{2}-3.2288=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{879}{2000} for a, 0 for b, and -3.2288 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{879}{2000}\left(-3.2288\right)}}{2\times \frac{879}{2000}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{879}{2000}\left(-3.2288\right)}}{2\times \frac{879}{2000}}$$

Multiply -4 times \frac{879}{2000}.

$$x=\frac{0±\sqrt{-\frac{879}{500}\left(-3.2288\right)}}{2\times \frac{879}{2000}}$$

Multiply -\frac{879}{500} times -3.2288 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{\frac{886911}{156250}}}{2\times \frac{879}{2000}}$$

Take the square root of \frac{886911}{156250}.

$$x=\frac{0±\frac{\sqrt{8869110}}{1250}}{2\times \frac{879}{2000}}$$

Multiply 2 times \frac{879}{2000}.

$$x=\frac{0±\frac{\sqrt{8869110}}{1250}}{\frac{879}{1000}}$$

Now solve the equation x=\frac{0±\frac{\sqrt{8869110}}{1250}}{\frac{879}{1000}} when ± is plus.

$$x=\frac{4\sqrt{8869110}}{4395}$$

Now solve the equation x=\frac{0±\frac{\sqrt{8869110}}{1250}}{\frac{879}{1000}} when ± is minus.

$$x=-\frac{4\sqrt{8869110}}{4395}$$

The equation is now solved.

$$x=\frac{4\sqrt{8869110}}{4395} x=-\frac{4\sqrt{8869110}}{4395}$$