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Solve for $k$ . $\newline$ $\sqrt{2k} = \sqrt{8k + 10}$ $\newline$ $k =$ _____

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Solve radical equations II

Full solution

Q. Solve for

k

.

\newline

\sqrt{2k} = \sqrt{8k + 10}

\newline

k =

_____

Square Roots Elimination: First, we need to eliminate the square roots by squaring both sides of the equation. $\newline$ $\sqrt{2k} = \sqrt{8k + 10}$ $\newline$ $(\sqrt{2k})^2 = (\sqrt{8k + 10})^2$ $\newline$ $2k = 8k + 10$
Variable Isolation: Next, we need to isolate the variable $k$ on one side of the equation. $2k = 8k + 10$ $2k - 8k = 8k + 10 - 8k$ $-6k = 10$
Dividing to Solve for k: Now, we divide both sides by $-6$ to solve for $k$ . $-6k = 10$ $k = \frac{10}{-6}$ $k = -\frac{5}{3}$

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