Solve 2-x+4/2=x^2-1/2(x+1)

$$2 - \frac { x + 4 } { 2 } = x ^ { 2 } - \frac { 1 } { 2 } ( x + 1 )$$

Solve for x

$$x=\frac{\sqrt{2}}{2}\approx 0.707106781$$

$$x=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

Steps by Finding Square Root

Multiply both sides of the equation by 2.

$$4-\left(x+4\right)=2x^{2}-\left(x+1\right)$$

To find the opposite of x+4, find the opposite of each term.

$$4-x-4=2x^{2}-\left(x+1\right)$$

Subtract 4 from 4 to get 0.

$$-x=2x^{2}-\left(x+1\right)$$

To find the opposite of x+1, find the opposite of each term.

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

Subtract 2x^{2} from both sides.

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

Add x to both sides.

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

Combine -x and x to get 0.

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

Divide both sides by -2.

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

Fraction \frac{-1}{-2} can be simplified to \frac{1}{2} by removing the negative sign from both the numerator and the denominator.

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

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$4-\left(x+4\right)=2x^{2}-\left(x+1\right)$$

To find the opposite of x+4, find the opposite of each term.

$$4-x-4=2x^{2}-\left(x+1\right)$$

Subtract 4 from 4 to get 0.

$$-x=2x^{2}-\left(x+1\right)$$

To find the opposite of x+1, find the opposite of each term.

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

Subtract 2x^{2} from both sides.

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

Add x to both sides.

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

Combine -x and x to get 0.

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

Add 1 to both sides.

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

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

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

Square 0.

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

Multiply -4 times -2.

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

Take the square root of 8.

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

Multiply 2 times -2.

$$x=\frac{0±2\sqrt{2}}{-4}$$

Now solve the equation x=\frac{0±2\sqrt{2}}{-4} when ± is plus.

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

Now solve the equation x=\frac{0±2\sqrt{2}}{-4} when ± is minus.

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

The equation is now solved.

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