Solve 18-x^2=34

$$18 - x ^ { 2 } = 34$$

Solve for x (complex solution)

$$x=4i$$

$$x=-4i$$

Steps by Finding Square Root

Subtract 18 from both sides.

$$-x^{2}=34-18$$

Subtract 18 from 34 to get 16.

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

Divide both sides by -1.

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

The equation is now solved.

$$x=4i x=-4i$$

Steps Using the Quadratic Formula

Subtract 34 from both sides.

$$18-x^{2}-34=0$$

Subtract 34 from 18 to get -16.

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

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.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-16\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-16\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-16\right)}}{2\left(-1\right)}$$

Multiply 4 times -16.

$$x=\frac{0±\sqrt{-64}}{2\left(-1\right)}$$

Take the square root of -64.

$$x=\frac{0±8i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±8i}{-2}$$

Now solve the equation x=\frac{0±8i}{-2} when ± is plus.

$$x=-4i$$

Now solve the equation x=\frac{0±8i}{-2} when ± is minus.

$$x=4i$$

The equation is now solved.

$$x=-4i x=4i$$