Solve x^2+25+19=-x^2

$${ x }^{ 2 } +25+19 = - { x }^{ 2 }$$

Solve for x (complex solution)

$$x=-\sqrt{22}i\approx -0-4.69041576i$$

$$x=\sqrt{22}i\approx 4.69041576i$$

Steps by Finding Square Root

Add 25 and 19 to get 44.

$$x^{2}+44=-x^{2}$$

Add x^{2} to both sides.

$$x^{2}+44+x^{2}=0$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}+44=0$$

Subtract 44 from both sides. Anything subtracted from zero gives its negation.

$$2x^{2}=-44$$

Divide both sides by 2.

$$x^{2}=\frac{-44}{2}$$

Divide -44 by 2 to get -22.

$$x^{2}=-22$$

The equation is now solved.

$$x=\sqrt{22}i x=-\sqrt{22}i$$

Steps Using the Quadratic Formula

Add 25 and 19 to get 44.

$$x^{2}+44=-x^{2}$$

Add x^{2} to both sides.

$$x^{2}+44+x^{2}=0$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}+44=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 44 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 44}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\times 44}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 44}}{2\times 2}$$

Multiply -8 times 44.

$$x=\frac{0±\sqrt{-352}}{2\times 2}$$

Take the square root of -352.

$$x=\frac{0±4\sqrt{22}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{22}i}{4}$$

Now solve the equation x=\frac{0±4\sqrt{22}i}{4} when ± is plus.

$$x=\sqrt{22}i$$

Now solve the equation x=\frac{0±4\sqrt{22}i}{4} when ± is minus.

$$x=-\sqrt{22}i$$

The equation is now solved.

$$x=\sqrt{22}i x=-\sqrt{22}i$$