Solve left(2x+1right)^2=4left(x+1right)^2

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

Solve for x

$$x=-\frac{3}{4}=-0.75$$

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}.

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

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

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

Use the distributive property to multiply 4 by x^{2}+2x+1.

$$4x^{2}+4x+1=4x^{2}+8x+4$$

Subtract 4x^{2} from both sides.

$$4x^{2}+4x+1-4x^{2}=8x+4$$

Combine 4x^{2} and -4x^{2} to get 0.

$$4x+1=8x+4$$

Subtract 8x from both sides.

$$4x+1-8x=4$$

Combine 4x and -8x to get -4x.

$$-4x+1=4$$

Subtract 1 from both sides.

$$-4x=4-1$$

Subtract 1 from 4 to get 3.

$$-4x=3$$

Divide both sides by -4.

$$x=\frac{3}{-4}$$

Fraction \frac{3}{-4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$x=-\frac{3}{4}$$