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$w=\sqrt{108w}$ $\newline$ What is the sum of all solutions to the given equation?

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Evaluate two-variable equations: word problems

Full solution

Q.

w=\sqrt{108w}

\newline

What is the sum of all solutions to the given equation?

Isolate $w$ by squaring: First, let's isolate $w$ in the equation by squaring both sides to eliminate the square root. $\newline$ $w = \sqrt{108 w}$ $\newline$ $w^2 = 108 w$
Rearrange to set to zero: Next, rearrange the equation to set it to zero, which is helpful for solving quadratic equations. $w^2 - 108w = 0$
Factor out common term: Factor out the common term, which is $w$ , from the equation. $w(w - 108) = 0$
Solve for w: Now, solve for w by setting each factor equal to zero. $\newline$ $w = 0$ or $w - 108 = 0$ $\newline$ $w = 0$ or $w = 108$
Find the sum: Finally, add the solutions together to find the sum. $\newline$ Sum = $0 + 108 = 108$

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