Solve (1-1/2x^2)=554.

$$( 1 - \frac { 1 } { 2 } x ^ { 2 } ) = 554 .$$

Solve for x (complex solution)

$$x=-\sqrt{1106}i\approx -0-33.256578297i$$

$$x=\sqrt{1106}i\approx 33.256578297i$$

Steps by Finding Square Root

Subtract 1 from both sides.

$$-\frac{1}{2}x^{2}=554-1$$

Subtract 1 from 554 to get 553.

$$-\frac{1}{2}x^{2}=553$$

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

$$x^{2}=553\left(-2\right)$$

Multiply 553 and -2 to get -1106.

$$x^{2}=-1106$$

The equation is now solved.

$$x=\sqrt{1106}i x=-\sqrt{1106}i$$

Steps Using the Quadratic Formula

Subtract 554 from both sides.

$$1-\frac{1}{2}x^{2}-554=0$$

Subtract 554 from 1 to get -553.

$$-553-\frac{1}{2}x^{2}=0$$

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.

$$-\frac{1}{2}x^{2}-553=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{1}{2} for a, 0 for b, and -553 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{2}\right)\left(-553\right)}}{2\left(-\frac{1}{2}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{2}\right)\left(-553\right)}}{2\left(-\frac{1}{2}\right)}$$

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

$$x=\frac{0±\sqrt{2\left(-553\right)}}{2\left(-\frac{1}{2}\right)}$$

Multiply 2 times -553.

$$x=\frac{0±\sqrt{-1106}}{2\left(-\frac{1}{2}\right)}$$

Take the square root of -1106.

$$x=\frac{0±\sqrt{1106}i}{2\left(-\frac{1}{2}\right)}$$

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

$$x=\frac{0±\sqrt{1106}i}{-1}$$

Now solve the equation x=\frac{0±\sqrt{1106}i}{-1} when ± is plus.

$$x=-\sqrt{1106}i$$

Now solve the equation x=\frac{0±\sqrt{1106}i}{-1} when ± is minus.

$$x=\sqrt{1106}i$$

The equation is now solved.

$$x=-\sqrt{1106}i x=\sqrt{1106}i$$