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

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

Solve for x

$$x = \frac{25}{8} = 3\frac{1}{8} = 3.125$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$-16+8x=9$$

Add 16 to both sides.

$$8x=9+16$$

Add 9 and 16 to get 25.

$$8x=25$$

Divide both sides by 8.

$$x=\frac{25}{8}$$