Solve 2/5x^2+4=9

$$\frac{ 2 }{ 5 } { x }^{ 2 } +4=9$$

Solve for x

$$x = \frac{5 \sqrt{2}}{2} \approx 3.535533906$$

$$x = -\frac{5 \sqrt{2}}{2} \approx -3.535533906$$

Steps by Finding Square Root

Subtract 4 from both sides.

$$\frac{2}{5}x^{2}=9-4$$

Subtract 4 from 9 to get 5.

$$\frac{2}{5}x^{2}=5$$

Multiply both sides by \frac{5}{2}, the reciprocal of \frac{2}{5}.

$$x^{2}=5\times \frac{5}{2}$$

Multiply 5 and \frac{5}{2} to get \frac{25}{2}.

$$x^{2}=\frac{25}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{5\sqrt{2}}{2} x=-\frac{5\sqrt{2}}{2}$$

Steps Using the Quadratic Formula

Subtract 9 from both sides.

$$\frac{2}{5}x^{2}+4-9=0$$

Subtract 9 from 4 to get -5.

$$\frac{2}{5}x^{2}-5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{2}{5} for a, 0 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{2}{5}\left(-5\right)}}{2\times \frac{2}{5}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{2}{5}\left(-5\right)}}{2\times \frac{2}{5}}$$

Multiply -4 times \frac{2}{5}.

$$x=\frac{0±\sqrt{-\frac{8}{5}\left(-5\right)}}{2\times \frac{2}{5}}$$

Multiply -\frac{8}{5} times -5.

$$x=\frac{0±\sqrt{8}}{2\times \frac{2}{5}}$$

Take the square root of 8.

$$x=\frac{0±2\sqrt{2}}{2\times \frac{2}{5}}$$

Multiply 2 times \frac{2}{5}.

$$x=\frac{0±2\sqrt{2}}{\frac{4}{5}}$$

Now solve the equation x=\frac{0±2\sqrt{2}}{\frac{4}{5}} when ± is plus.

$$x=\frac{5\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{2}}{\frac{4}{5}} when ± is minus.

$$x=-\frac{5\sqrt{2}}{2}$$

The equation is now solved.

$$x=\frac{5\sqrt{2}}{2} x=-\frac{5\sqrt{2}}{2}$$