Solve x^2-(x-3)^2=51

$$x ^ { 2 } - {( x - 3 )} ^ { 2 } = 51$$

Solve for x

$$x=10$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$x^{2}-\left(x^{2}-6x+9\right)=51$$

To find the opposite of x^{2}-6x+9, find the opposite of each term.

$$x^{2}-x^{2}+6x-9=51$$

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

$$6x-9=51$$

Add 9 to both sides.

$$6x=51+9$$

Add 51 and 9 to get 60.

$$6x=60$$

Divide both sides by 6.

$$x=\frac{60}{6}$$

Divide 60 by 6 to get 10.

$$x=10$$