Solve (8-x^2)-x^2=36

$$( 8 - x ^ { 2 } ) - x ^ { 2 } = 36$$

Solve for x (complex solution)

$$x=-\sqrt{14}i\approx -0-3.741657387i$$

$$x=\sqrt{14}i\approx 3.741657387i$$

Steps by Finding Square Root

Combine -x^{2} and -x^{2} to get -2x^{2}.

$$8-2x^{2}=36$$

Subtract 8 from both sides.

$$-2x^{2}=36-8$$

Subtract 8 from 36 to get 28.

$$-2x^{2}=28$$

Divide both sides by -2.

$$x^{2}=\frac{28}{-2}$$

Divide 28 by -2 to get -14.

$$x^{2}=-14$$

The equation is now solved.

$$x=\sqrt{14}i x=-\sqrt{14}i$$

Steps Using the Quadratic Formula

Combine -x^{2} and -x^{2} to get -2x^{2}.

$$8-2x^{2}=36$$

Subtract 36 from both sides.

$$8-2x^{2}-36=0$$

Subtract 36 from 8 to get -28.

$$-28-2x^{2}=0$$

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.

$$-2x^{2}-28=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and -28 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\left(-28\right)}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\left(-28\right)}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\left(-28\right)}}{2\left(-2\right)}$$

Multiply 8 times -28.

$$x=\frac{0±\sqrt{-224}}{2\left(-2\right)}$$

Take the square root of -224.

$$x=\frac{0±4\sqrt{14}i}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±4\sqrt{14}i}{-4}$$

Now solve the equation x=\frac{0±4\sqrt{14}i}{-4} when ± is plus.

$$x=-\sqrt{14}i$$

Now solve the equation x=\frac{0±4\sqrt{14}i}{-4} when ± is minus.

$$x=\sqrt{14}i$$

The equation is now solved.

$$x=-\sqrt{14}i x=\sqrt{14}i$$