Solve x_1^2=frac{4x_{1}+11}{y}

$$x _ { 1 } ^ { 2 } = \frac { 4 x _ { 1 } + 11 } { y }$$

Solve for y

$$y=\frac{4x_{1}+11}{x_{1}^{2}}$$

$$x_{1}\neq -\frac{11}{4}\text{ and }x_{1}\neq 0$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$yx_{1}^{2}=4x_{1}+11$$

The equation is in standard form.

$$x_{1}^{2}y=4x_{1}+11$$

Divide both sides by x_{1}^{2}.

$$\frac{x_{1}^{2}y}{x_{1}^{2}}=\frac{4x_{1}+11}{x_{1}^{2}}$$

Dividing by x_{1}^{2} undoes the multiplication by x_{1}^{2}.

$$y=\frac{4x_{1}+11}{x_{1}^{2}}$$

Variable y cannot be equal to 0.

$$y=\frac{4x_{1}+11}{x_{1}^{2}}\text{, }y\neq 0$$

Solve for x_1

$$x_{1}=\frac{\sqrt{11y+4}+2}{y}$$

$$x_{1}=\frac{-\sqrt{11y+4}+2}{y}\text{, }y\neq 0\text{ and }y\geq -\frac{4}{11}$$