Solve (x-3)^2-(x-4)^2=3

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

Solve for x

$$x=5$$

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}.

$$x^{2}-6x+9-\left(x-4\right)^{2}=3$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$x^{2}-6x+9-\left(x^{2}-8x+16\right)=3$$

To find the opposite of x^{2}-8x+16, find the opposite of each term.

$$x^{2}-6x+9-x^{2}+8x-16=3$$

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

$$-6x+9+8x-16=3$$

Combine -6x and 8x to get 2x.

$$2x+9-16=3$$

Subtract 16 from 9 to get -7.

$$2x-7=3$$

Add 7 to both sides.

$$2x=3+7$$

Add 3 and 7 to get 10.

$$2x=10$$

Divide both sides by 2.

$$x=\frac{10}{2}$$

Divide 10 by 2 to get 5.

$$x=5$$