Solve x^2+9=e

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

Solve for x (complex solution)

$$x=-i\sqrt{9-e}\approx -0-2.506335606i$$

$$x=i\sqrt{9-e}\approx 2.506335606i$$

Steps by Finding Square Root

Subtract 9 from both sides.

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

The equation is now solved.

$$x=i\sqrt{9-e} x=-i\sqrt{9-e}$$

Steps Using the Quadratic Formula

Subtract e from both sides.

$$x^{2}+9-e=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 9-e for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(9-e\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(9-e\right)}}{2}$$

Multiply -4 times 9-e.

$$x=\frac{0±\sqrt{4e-36}}{2}$$

Take the square root of -36+4e.

$$x=\frac{0±2i\sqrt{9-e}}{2}$$

Now solve the equation x=\frac{0±2i\sqrt{9-e}}{2} when ± is plus.

$$x=i\sqrt{9-e}$$

Now solve the equation x=\frac{0±2i\sqrt{9-e}}{2} when ± is minus.

$$x=-i\sqrt{9-e}$$

The equation is now solved.

$$x=i\sqrt{9-e} x=-i\sqrt{9-e}$$