Solve 5=-2(x^2-22+121)+23

$$5=-2( { x }^{ 2 } -22+121)+23$$

Solve for x (complex solution)

$$x=-3\sqrt{10}i\approx -0-9.486832981i$$

$$x=3\sqrt{10}i\approx 9.486832981i$$

Steps by Finding Square Root

Add -22 and 121 to get 99.

$$5=-2\left(x^{2}+99\right)+23$$

Use the distributive property to multiply -2 by x^{2}+99.

$$5=-2x^{2}-198+23$$

Add -198 and 23 to get -175.

$$5=-2x^{2}-175$$

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

$$-2x^{2}-175=5$$

Add 175 to both sides.

$$-2x^{2}=5+175$$

Add 5 and 175 to get 180.

$$-2x^{2}=180$$

Divide both sides by -2.

$$x^{2}=\frac{180}{-2}$$

Divide 180 by -2 to get -90.

$$x^{2}=-90$$

The equation is now solved.

$$x=3\sqrt{10}i x=-3\sqrt{10}i$$

Steps Using the Quadratic Formula

Add -22 and 121 to get 99.

$$5=-2\left(x^{2}+99\right)+23$$

Use the distributive property to multiply -2 by x^{2}+99.

$$5=-2x^{2}-198+23$$

Add -198 and 23 to get -175.

$$5=-2x^{2}-175$$

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

$$-2x^{2}-175=5$$

Subtract 5 from both sides.

$$-2x^{2}-175-5=0$$

Subtract 5 from -175 to get -180.

$$-2x^{2}-180=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and -180 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\left(-180\right)}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\left(-180\right)}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\left(-180\right)}}{2\left(-2\right)}$$

Multiply 8 times -180.

$$x=\frac{0±\sqrt{-1440}}{2\left(-2\right)}$$

Take the square root of -1440.

$$x=\frac{0±12\sqrt{10}i}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±12\sqrt{10}i}{-4}$$

Now solve the equation x=\frac{0±12\sqrt{10}i}{-4} when ± is plus.

$$x=-3\sqrt{10}i$$

Now solve the equation x=\frac{0±12\sqrt{10}i}{-4} when ± is minus.

$$x=3\sqrt{10}i$$

The equation is now solved.

$$x=-3\sqrt{10}i x=3\sqrt{10}i$$