Solve (2x-1)^2+(x+1)^2=5x^2

$$( 2 x - 1 ) ^ { 2 } + ( x + 1 ) ^ { 2 } = 5 x ^ { 2 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

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

$$4x^{2}-4x+1+\left(x+1\right)^{2}=5x^{2}$$

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

$$4x^{2}-4x+1+x^{2}+2x+1=5x^{2}$$

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$5x^{2}-4x+1+2x+1=5x^{2}$$

Combine -4x and 2x to get -2x.

$$5x^{2}-2x+1+1=5x^{2}$$

Add 1 and 1 to get 2.

$$5x^{2}-2x+2=5x^{2}$$

Subtract 5x^{2} from both sides.

$$5x^{2}-2x+2-5x^{2}=0$$

Combine 5x^{2} and -5x^{2} to get 0.

$$-2x+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-2x=-2$$

Divide both sides by -2.

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

Divide -2 by -2 to get 1.

$$x=1$$