Solve 9^2=36-16x^2

$$9 ^ { 2 } = 36 - 16 x ^ { 2 }$$

Solve for x (complex solution)

$$x=-\frac{3\sqrt{5}i}{4}\approx -0-1.677050983i$$

$$x=\frac{3\sqrt{5}i}{4}\approx 1.677050983i$$

Steps by Finding Square Root

Calculate 9 to the power of 2 and get 81.

$$81=36-16x^{2}$$

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

$$36-16x^{2}=81$$

Subtract 36 from both sides.

$$-16x^{2}=81-36$$

Subtract 36 from 81 to get 45.

$$-16x^{2}=45$$

Divide both sides by -16.

$$x^{2}=-\frac{45}{16}$$

The equation is now solved.

$$x=\frac{3\sqrt{5}i}{4} x=-\frac{3\sqrt{5}i}{4}$$

Steps Using the Quadratic Formula

Calculate 9 to the power of 2 and get 81.

$$81=36-16x^{2}$$

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

$$36-16x^{2}=81$$

Subtract 81 from both sides.

$$36-16x^{2}-81=0$$

Subtract 81 from 36 to get -45.

$$-45-16x^{2}=0$$

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.

$$-16x^{2}-45=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -16 for a, 0 for b, and -45 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-16\right)\left(-45\right)}}{2\left(-16\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-16\right)\left(-45\right)}}{2\left(-16\right)}$$

Multiply -4 times -16.

$$x=\frac{0±\sqrt{64\left(-45\right)}}{2\left(-16\right)}$$

Multiply 64 times -45.

$$x=\frac{0±\sqrt{-2880}}{2\left(-16\right)}$$

Take the square root of -2880.

$$x=\frac{0±24\sqrt{5}i}{2\left(-16\right)}$$

Multiply 2 times -16.

$$x=\frac{0±24\sqrt{5}i}{-32}$$

Now solve the equation x=\frac{0±24\sqrt{5}i}{-32} when ± is plus.

$$x=-\frac{3\sqrt{5}i}{4}$$

Now solve the equation x=\frac{0±24\sqrt{5}i}{-32} when ± is minus.

$$x=\frac{3\sqrt{5}i}{4}$$

The equation is now solved.

$$x=-\frac{3\sqrt{5}i}{4} x=\frac{3\sqrt{5}i}{4}$$