Solve {c}{x^2+x/2=(x-1)^2}{}

$$\left. \begin{array} { c } { x ^ { 2 } + \frac { x } { 2 } = ( x - 1 ) ^ { 2 } } \\ { } \end{array} \right.$$

Solve for x

$$x=\frac{2}{5}=0.4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

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

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

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

Use the distributive property to multiply 2 by x^{2}-2x+1.

$$2x^{2}+x=2x^{2}-4x+2$$

Subtract 2x^{2} from both sides.

$$2x^{2}+x-2x^{2}=-4x+2$$

Combine 2x^{2} and -2x^{2} to get 0.

$$x=-4x+2$$

Add 4x to both sides.

$$x+4x=2$$

Combine x and 4x to get 5x.

$$5x=2$$

Divide both sides by 5.

$$x=\frac{2}{5}$$