Solve pi1/x-x=5

$$\pi \frac { 1 } { x } - x = 5$$

Solve for x

$$x=\frac{-\sqrt{4\pi +25}-5}{2}\approx -5.56457055$$

$$x=\frac{\sqrt{4\pi +25}-5}{2}\approx 0.56457055$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\pi \times 1-xx=5x$$

Multiply x and x to get x^{2}.

$$\pi \times 1-x^{2}=5x$$

Subtract 5x from both sides.

$$\pi \times 1-x^{2}-5x=0$$

Reorder the terms.

$$-x^{2}-5x+\pi =0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, -5 for b, and \pi for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\left(-1\right)\pi }}{2\left(-1\right)}$$

Square -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\left(-1\right)\pi }}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-\left(-5\right)±\sqrt{25+4\pi }}{2\left(-1\right)}$$

Add 25 to 4\pi .

$$x=\frac{-\left(-5\right)±\sqrt{4\pi +25}}{2\left(-1\right)}$$

The opposite of -5 is 5.

$$x=\frac{5±\sqrt{4\pi +25}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{5±\sqrt{4\pi +25}}{-2}$$

Now solve the equation x=\frac{5±\sqrt{4\pi +25}}{-2} when ± is plus. Add 5 to \sqrt{25+4\pi }.

$$x=\frac{\sqrt{4\pi +25}+5}{-2}$$

Divide 5+\sqrt{25+4\pi } by -2.

$$x=\frac{-\sqrt{4\pi +25}-5}{2}$$

Now solve the equation x=\frac{5±\sqrt{4\pi +25}}{-2} when ± is minus. Subtract \sqrt{25+4\pi } from 5.

$$x=\frac{-\sqrt{4\pi +25}+5}{-2}$$

Divide 5-\sqrt{25+4\pi } by -2.

$$x=\frac{\sqrt{4\pi +25}-5}{2}$$

The equation is now solved.

$$x=\frac{-\sqrt{4\pi +25}-5}{2} x=\frac{\sqrt{4\pi +25}-5}{2}$$

Variable x cannot be equal to 0.

$$x=\frac{\sqrt{4\pi +25}-5}{2}\text{, }x\neq 0 x=\frac{-\sqrt{4\pi +25}-5}{2}\text{, }x\neq 0$$