Solve 1+x/2=1/4-4x

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

Solve for x

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

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

Steps by Finding Square Root

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 4\left(x-1\right), the least common multiple of 2,4-4x.

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

Use the distributive property to multiply 2x-2 by 1+x and combine like terms.

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

Add 2 to both sides.

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

Add -1 and 2 to get 1.

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

Divide both sides by 2.

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

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

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 4\left(x-1\right), the least common multiple of 2,4-4x.

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

Use the distributive property to multiply 2x-2 by 1+x and combine like terms.

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

Add 1 to both sides.

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

Add -2 and 1 to get -1.

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

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}.

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

Square 0.

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

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-1\right)}}{2\times 2}$$

Multiply -8 times -1.

$$x=\frac{0±\sqrt{8}}{2\times 2}$$

Take the square root of 8.

$$x=\frac{0±2\sqrt{2}}{2\times 2}$$

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.

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