Solve a+b+a/10+a^2+a/5=1

$$a + b + \frac { a } { 10 } + a ^ { 2 } + \frac { a } { 5 } = 1$$

Solve for b

$$b=-a^{2}-\frac{13a}{10}+1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 10,5.

$$10a+10b+a+10a^{2}+2a=10$$

Combine 10a and a to get 11a.

$$11a+10b+10a^{2}+2a=10$$

Combine 11a and 2a to get 13a.

$$13a+10b+10a^{2}=10$$

Subtract 13a from both sides.

$$10b+10a^{2}=10-13a$$

Subtract 10a^{2} from both sides.

$$10b=10-13a-10a^{2}$$

Divide both sides by 10.

$$\frac{10b}{10}=\frac{10-13a-10a^{2}}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$b=\frac{10-13a-10a^{2}}{10}$$

Divide 10-13a-10a^{2} by 10.

$$b=-a^{2}-\frac{13a}{10}+1$$

Solve for a (complex solution)

$$a=\frac{\sqrt{569-400b}-13}{20}$$

$$a=\frac{-\sqrt{569-400b}-13}{20}$$

Solve for a

$$a=\frac{\sqrt{569-400b}-13}{20}$$

$$a=\frac{-\sqrt{569-400b}-13}{20}\text{, }b\leq \frac{569}{400}$$