Solve for v. sqrt –v = sqrt ( 10 + v) v = _____

Square both sides: Square both sides of the equation to eliminate the square roots. (sqrt(–v))^2 = (sqrt(10 + v))^2 –v = 10 + vAdd v terms: Add v to both sides to get all v terms on one side. –v + v = 10 + v + v 0 = 10 + 2vIsolate term with v: Subtract 10 from both sides to isolate the term with v. 0 - 10 = 10 + 2v - 10 –10 = 2vSolve for v: Divide both sides by 2 to solve for v. –10 / 2 = 2v / 2 –5 = v

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Solve for $v$ . $\newline$ $\sqrt{-v} = \sqrt{10 + v}$ $\newline$ $v =$ _____

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Precalculus

Solve radical equations

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Q. Solve for

v

\newline

\sqrt{-v} = \sqrt{10 + v}

\newline

v =

_____

Square both sides: Square both sides of the equation to eliminate the square roots. $\newline$ $(\sqrt{-v})^2 = (\sqrt{10 + v})^2$ $\newline$ $-v = 10 + v$
Add $v$ terms: Add $v$ to both sides to get all $v$ terms on one side. $\newline$ $-v + v = 10 + v + v$ $\newline$ $0 = 10 + 2v$
Isolate term with v: Subtract $10$ from both sides to isolate the term with v. $\newline$ $0 - 10 = 10 + 2v - 10$ $\newline$ $–10 = 2v$
Solve for v: Divide both sides by $2$ to solve for v. $\newline$ $-10 / 2 = 2v / 2$ $\newline$ $-5 = v$