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

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Solve radical equations II

Full solution

Q. Solve for

s

.

\newline

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

\newline

s =

_____

Equation Simplification: First, we have the equation: $\newline$ $\sqrt{2s} = \sqrt{8s + 10}$ $\newline$ To eliminate the square roots, we square both sides of the equation: $\newline$ $(\sqrt{2s})^2 = (\sqrt{8s + 10})^2$ $\newline$ This simplifies to: $\newline$ $2s = 8s + 10$
Variable Isolation: Next, we need to isolate the variable $s$ on one side of the equation. We can do this by subtracting $8s$ from both sides: $2s - 8s = 8s + 10 - 8s$ This simplifies to: $-6s = 10$
Final Solution: Now, we divide both sides by $-6$ to solve for $s$ : $s = \frac{10}{-6}$ This simplifies to: $s = -\frac{5}{3}$ or $s = -1.666\ldots$

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