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Solve for $p$ . $\newline$ $\sqrt{4p} = \sqrt{10 + 3p}$ $\newline$ $p =$ _____

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Solve radical equations II

Full solution

Q. Solve for

p

.

\newline

\sqrt{4p} = \sqrt{10 + 3p}

\newline

p =

_____

Given equation: We are given the equation: $\newline$ $\sqrt{4p} = \sqrt{10 + 3p}$ $\newline$ To eliminate the square roots, we square both sides of the equation: $\newline$ (\sqrt{\(4\)p})^\(2 = (\sqrt{ $10$ + $3$ p})^ $2$
Squaring both sides: After squaring both sides, we get: $\newline$ $4p = 10 + 3p$ $\newline$ Now, we need to isolate $p$ on one side of the equation to solve for it.
Isolating $p$ : Subtract $3p$ from both sides of the equation to get $p$ by itself: $\newline$ $4p - 3p = 10 + 3p - 3p$ $\newline$ This simplifies to: $\newline$ $p = 10$

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