Solve x^2=2y/y

$$x ^ { 2 } = \frac { 2 y } { y }$$

Solve for x (complex solution)

$$x=-\sqrt{2}\approx -1.414213562$$

$$x=\sqrt{2}\approx 1.414213562\text{, }y\neq 0$$

Steps by Finding Square Root

The equation is now solved.

$$x=\sqrt{2} x=-\sqrt{2}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}=2$$

Subtract 2 from both sides of the equation.

$$x^{2}-2=2-2$$

Subtracting 2 from itself leaves 0.

$$x^{2}-2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)}}{2}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8}}{2}$$

Take the square root of 8.

$$x=\frac{0±2\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{2}}{2} when ± is plus.

$$x=\sqrt{2}$$

Now solve the equation x=\frac{0±2\sqrt{2}}{2} when ± is minus.

$$x=-\sqrt{2}$$

The equation is now solved.

$$x=\sqrt{2} x=-\sqrt{2}$$

Solve for y (complex solution)

$$y\neq 0$$

$$\left(x=-\sqrt{2}\text{ or }x=\sqrt{2}\right)\text{ and }y\neq 0$$

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.

$$yx^{2}=2y$$

Subtract 2y from both sides.

$$yx^{2}-2y=0$$

Combine all terms containing y.

$$\left(x^{2}-2\right)y=0$$

Divide 0 by x^{2}-2.

$$y=0$$

Variable y cannot be equal to 0.

$$y\in \emptyset$$

Solve for y

$$y\neq 0$$

$$|x|=\sqrt{2}\text{ and }y\neq 0$$

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.

$$yx^{2}=2y$$

Subtract 2y from both sides.

$$yx^{2}-2y=0$$

Combine all terms containing y.

$$\left(x^{2}-2\right)y=0$$

Divide 0 by x^{2}-2.

$$y=0$$

Variable y cannot be equal to 0.

$$y\in \emptyset$$

Solve for x

$$x=\sqrt{2}$$

$$x=-\sqrt{2}\text{, }y\neq 0$$