Solve 9+2+x^2=5

$$9 + 2 + x ^ { 2 } = 5$$

Solve for x (complex solution)

$$x=-\sqrt{6}i\approx -0-2.449489743i$$

$$x=\sqrt{6}i\approx 2.449489743i$$

Steps by Finding Square Root

Add 9 and 2 to get 11.

$$11+x^{2}=5$$

Subtract 11 from both sides.

$$x^{2}=5-11$$

Subtract 11 from 5 to get -6.

$$x^{2}=-6$$

The equation is now solved.

$$x=\sqrt{6}i x=-\sqrt{6}i$$

Steps Using the Quadratic Formula

Add 9 and 2 to get 11.

$$11+x^{2}=5$$

Subtract 5 from both sides.

$$11+x^{2}-5=0$$

Subtract 5 from 11 to get 6.

$$6+x^{2}=0$$

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.

$$x^{2}+6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6}}{2}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24}}{2}$$

Take the square root of -24.

$$x=\frac{0±2\sqrt{6}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{6}i}{2} when ± is plus.

$$x=\sqrt{6}i$$

Now solve the equation x=\frac{0±2\sqrt{6}i}{2} when ± is minus.

$$x=-\sqrt{6}i$$

The equation is now solved.

$$x=\sqrt{6}i x=-\sqrt{6}i$$