Solve 65/16=25+169-x^2/130

$$\frac { 65 } { 16 } = \frac { 25 + 169 - x ^ { 2 } } { 130 }$$

Solve for x (complex solution)

$$x=-\frac{9\sqrt{66}i}{4}\approx -0-18.27908641i$$

$$x=\frac{9\sqrt{66}i}{4}\approx 18.27908641i$$

Steps by Finding Square Root

Multiply both sides by 130.

$$\frac{65}{16}\times 130=25+169-x^{2}$$

Multiply \frac{65}{16} and 130 to get \frac{4225}{8}.

$$\frac{4225}{8}=25+169-x^{2}$$

Add 25 and 169 to get 194.

$$\frac{4225}{8}=194-x^{2}$$

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

$$194-x^{2}=\frac{4225}{8}$$

Subtract 194 from both sides.

$$-x^{2}=\frac{4225}{8}-194$$

Subtract 194 from \frac{4225}{8} to get \frac{2673}{8}.

$$-x^{2}=\frac{2673}{8}$$

Divide both sides by -1.

$$x^{2}=\frac{\frac{2673}{8}}{-1}$$

Express \frac{\frac{2673}{8}}{-1} as a single fraction.

$$x^{2}=\frac{2673}{8\left(-1\right)}$$

Multiply 8 and -1 to get -8.

$$x^{2}=\frac{2673}{-8}$$

Fraction \frac{2673}{-8} can be rewritten as -\frac{2673}{8} by extracting the negative sign.

$$x^{2}=-\frac{2673}{8}$$

The equation is now solved.

$$x=\frac{9\sqrt{66}i}{4} x=-\frac{9\sqrt{66}i}{4}$$

Steps Using the Quadratic Formula

Multiply both sides by 130.

$$\frac{65}{16}\times 130=25+169-x^{2}$$

Multiply \frac{65}{16} and 130 to get \frac{4225}{8}.

$$\frac{4225}{8}=25+169-x^{2}$$

Add 25 and 169 to get 194.

$$\frac{4225}{8}=194-x^{2}$$

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

$$194-x^{2}=\frac{4225}{8}$$

Subtract \frac{4225}{8} from both sides.

$$194-x^{2}-\frac{4225}{8}=0$$

Subtract \frac{4225}{8} from 194 to get -\frac{2673}{8}.

$$-\frac{2673}{8}-x^{2}=0$$

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.

$$-x^{2}-\frac{2673}{8}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -\frac{2673}{8} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-\frac{2673}{8}\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-\frac{2673}{8}\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-\frac{2673}{8}\right)}}{2\left(-1\right)}$$

Multiply 4 times -\frac{2673}{8}.

$$x=\frac{0±\sqrt{-\frac{2673}{2}}}{2\left(-1\right)}$$

Take the square root of -\frac{2673}{2}.

$$x=\frac{0±\frac{9\sqrt{66}i}{2}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±\frac{9\sqrt{66}i}{2}}{-2}$$

Now solve the equation x=\frac{0±\frac{9\sqrt{66}i}{2}}{-2} when ± is plus.

$$x=-\frac{9\sqrt{66}i}{4}$$

Now solve the equation x=\frac{0±\frac{9\sqrt{66}i}{2}}{-2} when ± is minus.

$$x=\frac{9\sqrt{66}i}{4}$$

The equation is now solved.

$$x=-\frac{9\sqrt{66}i}{4} x=\frac{9\sqrt{66}i}{4}$$