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

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

Solve for x

$$x = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

Steps for Solving Linear Equation

Calculate 2 to the power of 2 and get 4.

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

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

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

To find the opposite of 4-4x+x^{2}, find the opposite of each term.

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

Subtract 4 from 1 to get -3.

$$4-x^{2}=-3+4x-x^{2}$$

Subtract 4x from both sides.

$$4-x^{2}-4x=-3-x^{2}$$

Add x^{2} to both sides.

$$4-x^{2}-4x+x^{2}=-3$$

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

$$4-4x=-3$$

Subtract 4 from both sides.

$$-4x=-3-4$$

Subtract 4 from -3 to get -7.

$$-4x=-7$$

Divide both sides by -4.

$$x=\frac{-7}{-4}$$

Fraction \frac{-7}{-4} can be simplified to \frac{7}{4} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{7}{4}$$