Solve left(x-+0.5right)^2-x^2=2^2

$${ \left(x-+0.5 \right) }^{ 2 } - { x }^{ 2 } = { 2 }^{ 2 }$$

Solve for x

$$x=-3.75$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-0.5\right)^{2}.

$$x^{2}-x+0.25-x^{2}=2^{2}$$

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

$$-x+0.25=2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$-x+0.25=4$$

Subtract 0.25 from both sides.

$$-x=4-0.25$$

Subtract 0.25 from 4 to get 3.75.

$$-x=3.75$$

Multiply both sides by -1.

$$x=-3.75$$