Solve x+y^2/2*a^3=106

$$\frac { x + y ^ { 2 } } { 2 } \times a ^ { 3 } = 106$$

Solve for x

$$x=-y^{2}+\frac{212}{a^{3}}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$\left(x+y^{2}\right)a^{3}=212$$

Use the distributive property to multiply x+y^{2} by a^{3}.

$$xa^{3}+y^{2}a^{3}=212$$

Subtract y^{2}a^{3} from both sides.

$$xa^{3}=212-y^{2}a^{3}$$

Reorder the terms.

$$xa^{3}=-y^{2}a^{3}+212$$

The equation is in standard form.

$$a^{3}x=212-y^{2}a^{3}$$

Divide both sides by a^{3}.

$$\frac{a^{3}x}{a^{3}}=\frac{212-y^{2}a^{3}}{a^{3}}$$

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

$$x=\frac{212-y^{2}a^{3}}{a^{3}}$$

Divide -y^{2}a^{3}+212 by a^{3}.

$$x=-y^{2}+\frac{212}{a^{3}}$$

Solve for a

$$a=\sqrt[3]{\frac{212}{x+y^{2}}}$$

$$x\neq -y^{2}$$