Solve 1/2x^2+2=1

$$\frac { 1 } { 2 } x ^ { 2 } + 2 = 1$$

Solve for x (complex solution)

$$x=-\sqrt{2}i\approx -0-1.414213562i$$

$$x=\sqrt{2}i\approx 1.414213562i$$

Steps by Finding Square Root

Subtract 2 from both sides.

$$\frac{1}{2}x^{2}=1-2$$

Subtract 2 from 1 to get -1.

$$\frac{1}{2}x^{2}=-1$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

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

The equation is now solved.

$$x=\sqrt{2}i x=-\sqrt{2}i$$

Steps Using the Quadratic Formula

Subtract 1 from both sides.

$$\frac{1}{2}x^{2}+2-1=0$$

Subtract 1 from 2 to get 1.

$$\frac{1}{2}x^{2}+1=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{2}}}{2\times \frac{1}{2}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{2}}}{2\times \frac{1}{2}}$$

Multiply -4 times \frac{1}{2}.

$$x=\frac{0±\sqrt{-2}}{2\times \frac{1}{2}}$$

Take the square root of -2.

$$x=\frac{0±\sqrt{2}i}{2\times \frac{1}{2}}$$

Multiply 2 times \frac{1}{2}.

$$x=\frac{0±\sqrt{2}i}{1}$$

Now solve the equation x=\frac{0±\sqrt{2}i}{1} when ± is plus.

$$x=\sqrt{2}i$$

Now solve the equation x=\frac{0±\sqrt{2}i}{1} when ± is minus.

$$x=-\sqrt{2}i$$

The equation is now solved.

$$x=\sqrt{2}i x=-\sqrt{2}i$$