Solve x^2-(x-1)^2=25

$$x ^ { 2 } - ( x - 1 ) ^ { 2 } = 25$$

Solve for x

$$x=13$$

Steps for Solving Linear Equation

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

$$x^{2}-\left(x^{2}-2x+1\right)=25$$

To find the opposite of x^{2}-2x+1, find the opposite of each term.

$$x^{2}-x^{2}+2x-1=25$$

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

$$2x-1=25$$

Add 1 to both sides.

$$2x=25+1$$

Add 25 and 1 to get 26.

$$2x=26$$

Divide both sides by 2.

$$x=\frac{26}{2}$$

Divide 26 by 2 to get 13.

$$x=13$$