Solve for x 2x^2-4y^2=16

$2 x^{2} - 4 y^{2} = 16$

Step 1

Add $4 y^{2}$ to both sides of the equation.

$2 x^{2} = 16 + 4 y^{2}$

Step 2

Divide each term in $2 x^{2} = 16 + 4 y^{2}$ by $2$ and simplify.

Divide each term in $2 x^{2} = 16 + 4 y^{2}$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{16}{2} + \frac{4 y^{2}}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{16}{2} + \frac{4 y^{2}}{2}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{16}{2} + \frac{4 y^{2}}{2}$

Simplify the right side.

Simplify each term.

Divide $16$ by $2$ .

$x^{2} = 8 + \frac{4 y^{2}}{2}$

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 y^{2}$ .

$x^{2} = 8 + \frac{2 (2 y^{2})}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$x^{2} = 8 + \frac{2 (2 y^{2})}{2 (1)}$

Cancel the common factor.

$x^{2} = 8 + \frac{2 (2 y^{2})}{2 \cdot 1}$

Rewrite the expression.

$x^{2} = 8 + \frac{2 y^{2}}{1}$

Divide $2 y^{2}$ by $1$ .

$x^{2} = 8 + 2 y^{2}$

Step 3

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{8 + 2 y^{2}}$

Step 4

Factor $2$ out of $8 + 2 y^{2}$ .

Factor $2$ out of $8$ .

$x = \pm \sqrt{2 \cdot 4 + 2 y^{2}}$

Factor $2$ out of $2 \cdot 4 + 2 y^{2}$ .

$x = \pm \sqrt{2 (4 + y^{2})}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{2 (4 + y^{2})}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{2 (4 + y^{2})}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{2 (4 + y^{2})}$

$x = - \sqrt{2 (4 + y^{2})}$

$x = \sqrt{2 (4 + y^{2})}$

$x = - \sqrt{2 (4 + y^{2})}$

Solve for x 2x^2-4y^2=16

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