Precalculus Examples

$\sqrt{2 y^{2} - 64} = y$

Step 1

Subtract $y$ from both sides of the equation.

$\sqrt{2 y^{2} - 64} - y = 0$

Step 2

Factor $2$ out of $2 y^{2} - 64$ .

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Step 2.1

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

$\sqrt{2 (y^{2}) - 64} - y = 0$

Step 2.2

Factor $2$ out of $- 64$ .

$\sqrt{2 y^{2} + 2 \cdot - 32} - y = 0$

Step 2.3

Factor $2$ out of $2 y^{2} + 2 \cdot - 32$ .

$\sqrt{2 (y^{2} - 32)} - y = 0$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$y = 8$

Step 4