Solve x^2+16=left(3+xright)^2

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

Solve for x

$$x = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$$

Steps for Solving Linear Equation

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

$$x^{2}+16=9+6x+x^{2}$$

Subtract 6x from both sides.

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

Subtract x^{2} from both sides.

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

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

$$16-6x=9$$

Subtract 16 from both sides.

$$-6x=9-16$$

Subtract 16 from 9 to get -7.

$$-6x=-7$$

Divide both sides by -6.

$$x=\frac{-7}{-6}$$

Fraction \frac{-7}{-6} can be simplified to \frac{7}{6} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{7}{6}$$