Solve -1/2x^2+2x+2=2x+2

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

Solve for x

$$x=0$$

Steps by Finding Square Root

Subtract 2x from both sides.

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

Combine 2x and -2x to get 0.

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

Subtract 2 from both sides.

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

Subtract 2 from 2 to get 0.

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

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

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

Subtract 2x from both sides.

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

Combine 2x and -2x to get 0.

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

Subtract 2 from both sides.

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

Subtract 2 from 2 to get 0.

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

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

$$x^{2}=0$$

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

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2}$$

Divide 0 by 2.

$$x=0$$