Solve 80+25/4+left(x+4right)^2=121/4+x^2

$$80+ \frac{ 25 }{ 4 } + { \left(x+4 \right) }^{ 2 } = \frac{ 121 }{ 4 } + { x }^{ 2 }$$

Solve for x

$$x=-9$$

Steps for Solving Linear Equation

Add 80 and \frac{25}{4} to get \frac{345}{4}.

$$\frac{345}{4}+\left(x+4\right)^{2}=\frac{121}{4}+x^{2}$$

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

$$\frac{345}{4}+x^{2}+8x+16=\frac{121}{4}+x^{2}$$

Add \frac{345}{4} and 16 to get \frac{409}{4}.

$$\frac{409}{4}+x^{2}+8x=\frac{121}{4}+x^{2}$$

Subtract x^{2} from both sides.

$$\frac{409}{4}+x^{2}+8x-x^{2}=\frac{121}{4}$$

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

$$\frac{409}{4}+8x=\frac{121}{4}$$

Subtract \frac{409}{4} from both sides.

$$8x=\frac{121}{4}-\frac{409}{4}$$

Subtract \frac{409}{4} from \frac{121}{4} to get -72.

$$8x=-72$$

Divide both sides by 8.

$$x=\frac{-72}{8}$$

Divide -72 by 8 to get -9.

$$x=-9$$