Solve (x-frac{sqrt{3}+1}{2})=frac{-4sqrt{3}+(sqrt{3}+1)^2}{4}

$$( x - \frac { \sqrt { 3 } + 1 } { 2 } ) = \frac { - 4 \sqrt { 3 } + ( \sqrt { 3 } + 1 ) ^ { 2 } } { 4 }$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$4x-2\left(\sqrt{3}+1\right)=-4\sqrt{3}+\left(\sqrt{3}+1\right)^{2}$$

Use the distributive property to multiply -2 by \sqrt{3}+1.

$$4x-2\sqrt{3}-2=-4\sqrt{3}+\left(\sqrt{3}+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{3}+1\right)^{2}.

$$4x-2\sqrt{3}-2=-4\sqrt{3}+\left(\sqrt{3}\right)^{2}+2\sqrt{3}+1$$

The square of \sqrt{3} is 3.

$$4x-2\sqrt{3}-2=-4\sqrt{3}+3+2\sqrt{3}+1$$

Add 3 and 1 to get 4.

$$4x-2\sqrt{3}-2=-4\sqrt{3}+4+2\sqrt{3}$$

Combine -4\sqrt{3} and 2\sqrt{3} to get -2\sqrt{3}.

$$4x-2\sqrt{3}-2=-2\sqrt{3}+4$$

Add 2\sqrt{3} to both sides.

$$4x-2=-2\sqrt{3}+4+2\sqrt{3}$$

Combine -2\sqrt{3} and 2\sqrt{3} to get 0.

$$4x-2=4$$

Add 2 to both sides.

$$4x=4+2$$

Add 4 and 2 to get 6.

$$4x=6$$

Divide both sides by 4.

$$x=\frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$x=\frac{3}{2}$$