Solve a_{1}a+a_{1}a^3=10

$$a _ { 1 } a + a _ { 1 } a ^ { 3 } = 10$$

Solve for a_1

$$a_{1}=\frac{10}{a^{3}+a}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Combine all terms containing a_{1}.

$$\left(a+a^{3}\right)a_{1}=10$$

The equation is in standard form.

$$\left(a^{3}+a\right)a_{1}=10$$

Divide both sides by a+a^{3}.

$$\frac{\left(a^{3}+a\right)a_{1}}{a^{3}+a}=\frac{10}{a^{3}+a}$$

Dividing by a+a^{3} undoes the multiplication by a+a^{3}.

$$a_{1}=\frac{10}{a^{3}+a}$$

Divide 10 by a+a^{3}.

$$a_{1}=\frac{10}{a\left(a^{2}+1\right)}$$

Solve for a

$$a=\sqrt[3]{\frac{1}{9a_{1}|a_{1}|}}\left(\sqrt[3]{a_{1}\sqrt{3\left(a_{1}^{2}+675\right)}+45|a_{1}|}+\sqrt[3]{-a_{1}\sqrt{3\left(a_{1}^{2}+675\right)}+45|a_{1}|}\right)$$