Basic Math Examples

$\sqrt{2 y - 4} + \sqrt{20 y + 25} = \sqrt{30 y + 61}$

Step 1

Simplify each term.

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Step 1.1

Factor $2$ out of $2 y - 4$ .

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Step 1.1.1

Factor $2$ out of $2 y$ .

$\sqrt{2 (y) - 4} + \sqrt{20 y + 25} = \sqrt{30 y + 61}$

Step 1.1.2

Factor $2$ out of $- 4$ .

$\sqrt{2 y + 2 \cdot - 2} + \sqrt{20 y + 25} = \sqrt{30 y + 61}$

Step 1.1.3

Factor $2$ out of $2 y + 2 \cdot - 2$ .

$\sqrt{2 (y - 2)} + \sqrt{20 y + 25} = \sqrt{30 y + 61}$

Step 1.2

Factor $5$ out of $20 y + 25$ .

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Step 1.2.1

Factor $5$ out of $20 y$ .

$\sqrt{2 (y - 2)} + \sqrt{5 (4 y) + 25} = \sqrt{30 y + 61}$

Step 1.2.2

Factor $5$ out of $25$ .

$\sqrt{2 (y - 2)} + \sqrt{5 (4 y) + 5 (5)} = \sqrt{30 y + 61}$

Step 1.2.3

Factor $5$ out of $5 (4 y) + 5 (5)$ .

$\sqrt{2 (y - 2)} + \sqrt{5 (4 y + 5)} = \sqrt{30 y + 61}$

Step 2

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

$y = 10$

Step 3