sqrtt+5t=6sqrtt What is the sum of all solutions to the given equation?

Isolate square root term: First, isolate the square root term. Subtract $\sqrt{t}$ from both sides: $\sqrt{t} + 5t - \sqrt{t} = 6\sqrt{t} - \sqrt{t}$ This simplifies to: $5t = 5\sqrt{t}$Divide and simplify: Divide both sides by 5: $t = \sqrt{t}$Square both sides: Square both sides to remove the square root: $t^2 = t$Rearrange equation: Rearrange the equation to set it to zero: $t^2 - t = 0$Factor out: Factor out $t$: $t(t - 1) = 0$Solve for t: Set each factor to zero and solve for $t$: $t = 0$ or $t - 1 = 0$ So, $t = 0$ or $t = 1$Sum solutions: Sum the solutions: $0 + 1 = 1$

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sqrtt+5t=6sqrtt
What is the sum of all solutions to the given equation?

$\sqrt{t}+5 t=6 \sqrt{t}$ $\newline$ What is the sum of all solutions to the given equation?

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Algebra 2

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\sqrt{t}+5 t=6 \sqrt{t}

\newline

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

Isolate square root term: First, isolate the square root term. Subtract $\sqrt{t}$ from both sides: $\newline$ $\sqrt{t} + 5t - \sqrt{t} = 6\sqrt{t} - \sqrt{t}$ $\newline$ This simplifies to: $\newline$ $5t = 5\sqrt{t}$
Divide and simplify: Divide both sides by $5$ : $\newline$ $t = \sqrt{t}$
Square both sides: Square both sides to remove the square root: $\newline$ $t^2 = t$
Rearrange equation: Rearrange the equation to set it to zero: $\newline$ $t^2 - t = 0$
Factor out: Factor out $t$ : $\newline$ $t(t - 1) = 0$
Solve for t: Set each factor to zero and solve for $t$ : $\newline$ $t = 0$ or $t - 1 = 0$ $\newline$ So, $t = 0$ or $t = 1$
Sum solutions: Sum the solutions: $\newline$ $0 + 1 = 1$