Solve 100^2-left(55+xright)^2=65^2-x^2

$${ 100 }^{ 2 } - { \left(55+x \right) }^{ 2 } = { 65 }^{ 2 } - { x }^{ 2 }$$

Solve for x

$$x=25$$

Steps for Solving Linear Equation

Calculate 100 to the power of 2 and get 10000.

$$10000-\left(55+x\right)^{2}=65^{2}-x^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(55+x\right)^{2}.

$$10000-\left(3025+110x+x^{2}\right)=65^{2}-x^{2}$$

To find the opposite of 3025+110x+x^{2}, find the opposite of each term.

$$10000-3025-110x-x^{2}=65^{2}-x^{2}$$

Subtract 3025 from 10000 to get 6975.

$$6975-110x-x^{2}=65^{2}-x^{2}$$

Calculate 65 to the power of 2 and get 4225.

$$6975-110x-x^{2}=4225-x^{2}$$

Add x^{2} to both sides.

$$6975-110x-x^{2}+x^{2}=4225$$

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

$$6975-110x=4225$$

Subtract 6975 from both sides.

$$-110x=4225-6975$$

Subtract 6975 from 4225 to get -2750.

$$-110x=-2750$$

Divide both sides by -110.

$$x=\frac{-2750}{-110}$$

Divide -2750 by -110 to get 25.

$$x=25$$