Solve for w. sqrt ( 2w + 7) = sqrt –5w w = _____

Square both sides: Square both sides of the equation to eliminate the square roots. (sqrt(2w + 7))^2 = (sqrt(−5w))^2 2w + 7 = −5wAdd w terms: Add 5w to both sides of the equation to get all the w terms on one side. 2w + 5w + 7 = −5w + 5w 7w + 7 = 0Isolate the w term: Subtract 7 from both sides of the equation to isolate the w term. 7w + 7 - 7 = 0 - 7 7w = -7Divide to solve: Divide both sides of the equation by 7 to solve for w. 7w / 7 = -7 / 7 w = -1

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Solve for $w$ . $\newline$ $\sqrt{2w + 7} = \sqrt{-5w}$ $\newline$ $w =$ _____

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Q. Solve for

w

\newline

\sqrt{2w + 7} = \sqrt{-5w}

\newline

w =

_____

Square both sides: Square both sides of the equation to eliminate the square roots. $\newline$ $(\sqrt{2w + 7})^2 = (\sqrt{-5w})^2$ $\newline$ $2w + 7 = -5w$
Add $w$ terms: Add $5w$ to both sides of the equation to get all the $w$ terms on one side. $\newline$ $2w + 5w + 7 = -5w + 5w$ $\newline$ $7w + 7 = 0$
Isolate the w term: Subtract $7$ from both sides of the equation to isolate the w term. $\newline$ $7w + 7 - 7 = 0 - 7$ $\newline$ $7w = -7$
Divide to solve: Divide both sides of the equation by $7$ to solve for $w$ . $\frac{7w}{7} = \frac{-7}{7}$ $w = -1$