Solve 5x^2+72/23=2

$$5 { x }^{ 2 } + \frac{ 72 }{ 23 } =2$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2990}i}{115}\approx -0-0.475486021i$$

$$x=\frac{\sqrt{2990}i}{115}\approx 0.475486021i$$

Steps by Finding Square Root

Subtract \frac{72}{23} from both sides.

$$5x^{2}=2-\frac{72}{23}$$

Subtract \frac{72}{23} from 2 to get -\frac{26}{23}.

$$5x^{2}=-\frac{26}{23}$$

Divide both sides by 5.

$$x^{2}=\frac{-\frac{26}{23}}{5}$$

Express \frac{-\frac{26}{23}}{5} as a single fraction.

$$x^{2}=\frac{-26}{23\times 5}$$

Multiply 23 and 5 to get 115.

$$x^{2}=\frac{-26}{115}$$

Fraction \frac{-26}{115} can be rewritten as -\frac{26}{115} by extracting the negative sign.

$$x^{2}=-\frac{26}{115}$$

The equation is now solved.

$$x=\frac{\sqrt{2990}i}{115} x=-\frac{\sqrt{2990}i}{115}$$

Steps Using the Quadratic Formula

Subtract 2 from both sides.

$$5x^{2}+\frac{72}{23}-2=0$$

Subtract 2 from \frac{72}{23} to get \frac{26}{23}.

$$5x^{2}+\frac{26}{23}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and \frac{26}{23} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\times \frac{26}{23}}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\times \frac{26}{23}}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\times \frac{26}{23}}}{2\times 5}$$

Multiply -20 times \frac{26}{23}.

$$x=\frac{0±\sqrt{-\frac{520}{23}}}{2\times 5}$$

Take the square root of -\frac{520}{23}.

$$x=\frac{0±\frac{2\sqrt{2990}i}{23}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±\frac{2\sqrt{2990}i}{23}}{10}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{2990}i}{23}}{10} when ± is plus.

$$x=\frac{\sqrt{2990}i}{115}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{2990}i}{23}}{10} when ± is minus.

$$x=-\frac{\sqrt{2990}i}{115}$$

The equation is now solved.

$$x=\frac{\sqrt{2990}i}{115} x=-\frac{\sqrt{2990}i}{115}$$