Solve x-9-x-x^2=11

$$x - 9 - x - x ^ { 2 } = 11$$

Solve for x (complex solution)

$$x=-2\sqrt{5}i\approx -0-4.472135955i$$

$$x=2\sqrt{5}i\approx 4.472135955i$$

Steps by Finding Square Root

Combine x and -x to get 0.

$$-9-x^{2}=11$$

Add 9 to both sides.

$$-x^{2}=11+9$$

Add 11 and 9 to get 20.

$$-x^{2}=20$$

Divide both sides by -1.

$$x^{2}=-20$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Combine x and -x to get 0.

$$-9-x^{2}=11$$

Subtract 11 from both sides.

$$-9-x^{2}-11=0$$

Subtract 11 from -9 to get -20.

$$-20-x^{2}=0$$

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.

$$-x^{2}-20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-20\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-20\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-20\right)}}{2\left(-1\right)}$$

Multiply 4 times -20.

$$x=\frac{0±\sqrt{-80}}{2\left(-1\right)}$$

Take the square root of -80.

$$x=\frac{0±4\sqrt{5}i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±4\sqrt{5}i}{-2}$$

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

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

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

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

The equation is now solved.

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