Solve 4pi-x^2pi=9.5

$$4 \pi - x ^ { 2 } \pi = 9.5$$

Solve for x (complex solution)

$$x=-\sqrt{-\frac{19}{2\pi }+4}\approx -0.987955506$$

$$x=\sqrt{-\frac{19}{2\pi }+4}\approx 0.987955506$$

Steps by Finding Square Root

Subtract 4\pi from both sides.

$$-x^{2}\pi =9.5-4\pi$$

Dividing by -\pi undoes the multiplication by -\pi .

$$x^{2}=\frac{9.5-4\pi }{-\pi }$$

Divide 9.5-4\pi by -\pi .

$$x^{2}=-\frac{19}{2\pi }+4$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{16\pi -38}}{2\sqrt{\pi }} x=-\frac{\sqrt{16\pi -38}}{2\sqrt{\pi }}$$

Steps Using the Quadratic Formula

Subtract 9.5 from both sides.

$$4\pi -x^{2}\pi -9.5=0$$

Reorder the terms.

$$-\pi x^{2}+4\pi -9.5=0$$

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.

$$\left(-\pi \right)x^{2}+4\pi -9.5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\pi for a, 0 for b, and 4\pi -9.5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\pi \right)\left(4\pi -9.5\right)}}{2\left(-\pi \right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\pi \right)\left(4\pi -9.5\right)}}{2\left(-\pi \right)}$$

Multiply -4 times -\pi .

$$x=\frac{0±\sqrt{4\pi \left(4\pi -9.5\right)}}{2\left(-\pi \right)}$$

Take the square root of 4\pi \left(4\pi -9.5\right).

$$x=\frac{0±2\sqrt{\pi \left(4\pi -9.5\right)}}{2\left(-\pi \right)}$$

Multiply 2 times -\pi .

$$x=\frac{0±2\sqrt{\pi \left(4\pi -9.5\right)}}{-2\pi }$$

Now solve the equation x=\frac{0±2\sqrt{\pi \left(4\pi -9.5\right)}}{-2\pi } when ± is plus.

$$x=-\frac{\sqrt{4\pi -9.5}}{\sqrt{\pi }}$$

Now solve the equation x=\frac{0±2\sqrt{\pi \left(4\pi -9.5\right)}}{-2\pi } when ± is minus.

$$x=\frac{\sqrt{4\pi -9.5}}{\sqrt{\pi }}$$

The equation is now solved.

$$x=-\frac{\sqrt{4\pi -9.5}}{\sqrt{\pi }} x=\frac{\sqrt{4\pi -9.5}}{\sqrt{\pi }}$$

Solve for x

$$x=\frac{\sqrt{-\frac{38}{\pi }+16}}{2}\approx 0.987955506$$

$$x=-\frac{\sqrt{-\frac{38}{\pi }+16}}{2}\approx -0.987955506$$