Solve the following equation for y. y=◻=sqrt(3y^(2)-10 y)

Square both sides: We have the equation y = sqrt(3y^2 - 10y). To solve for y, we need to square both sides of the equation to eliminate the square root. (y)^2 = (sqrt(3y^2 - 10y))^2Combine like terms: Squaring both sides gives us: y^2 = 3y^2 - 10yFactor out common term: To solve for y, we need to move all terms involving y to one side of the equation to set it to zero. y^2 - 3y^2 + 10y = 0Set each factor equal to zero: Simplify the equation by combining like terms. -2y^2 + 10y = 0Solve for y: Factor out the common term y. y(-2y + 10) = 0Check solutions: Set each factor equal to zero and solve for y. y = 0 or -2y + 10 = 0Solve the second equation for y. -2y + 10 = 0 -2y = -10 y = 5We have two solutions for y, y = 0 and y = 5. However, we need to check if both solutions satisfy the original equation.Check y = 0 in the original equation. 0 = sqrt(3(0)^2 - 10(0)) 0 = sqrt(0) 0 = 0 This solution is valid.Check y = 5 in the original equation. 5 = sqrt(3(5)^2 - 10(5)) 5 = sqrt(75 - 50) 5 = sqrt(25) 5 = 5 This solution is also valid.

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Solve the following equation for
y.

y=◻=sqrt(3y^(2)-10 y)

Solve the following equation for $y$ . $\newline$ $\begin{array}{l} 2 y-3=\sqrt{3 y^{2}-10 x} \\ y=\square \end{array}$

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Algebra 1

Domain and range of square root functions: equations

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Q. Solve the following equation for

y

\newline

\begin{array}{l} 2 y-3=\sqrt{3 y^{2}-10 x} \\ y=\square \end{array}

Square both sides: We have the equation $y = \sqrt{3y^2 - 10y}$ . To solve for $y$ , we need to square both sides of the equation to eliminate the square root. $\newline$ $(y)^2 = (\sqrt{3y^2 - 10y})^2$
Combine like terms: Squaring both sides gives us: $y^2 = 3y^2 - 10y$
Factor out common term: To solve for $y$ , we need to move all terms involving $y$ to one side of the equation to set it to zero. $\newline$ $y^2 - 3y^2 + 10y = 0$
Set each factor equal to zero: Simplify the equation by combining like terms. $-2y^2 + 10y = 0$
Solve for y: Factor out the common term y. $\newline$ $y(-2y + 10) = 0$
Check solutions: Set each factor equal to zero and solve for $y$ . $y = 0$ or $-2y + 10 = 0$
Check solutions: Set each factor equal to zero and solve for $y$ .
$y = 0$ or $-2y + 10 = 0$ Solve the second equation for $y$ .
$-2y + 10 = 0$
$-2y = -10$
$y = 5$
Check solutions: Set each factor equal to zero and solve for $y$ .
$y = 0$ or $-2y + 10 = 0$ Solve the second equation for $y$ .
$-2y + 10 = 0$
$-2y = -10$
$y = 5$ We have two solutions for $y$ , $y = 0$ and $y = 5$ . However, we need to check if both solutions satisfy the original equation.
Check solutions: Set each factor equal to zero and solve for $y$ .
$y = 0$ or $-2y + 10 = 0$ Solve the second equation for $y$ .
$-2y + 10 = 0$
$-2y = -10$
$y = 5$ We have two solutions for $y$ , $y = 0$ and $y = 5$ . However, we need to check if both solutions satisfy the original equation.
Check $y = 0$ in the original equation.
$y = 0$ $1$
$y = 0$ $2$
$y = 0$ $3$
This solution is valid.
Check solutions: Set each factor equal to zero and solve for $y$ .
$y = 0$ or $-2y + 10 = 0$ Solve the second equation for $y$ .
$-2y + 10 = 0$
$-2y = -10$
$y = 5$ We have two solutions for $y$ , $y = 0$ and $y = 5$ . However, we need to check if both solutions satisfy the original equation.
Check $y = 0$ in the original equation.
$y = 0$ $1$
$y = 0$ $2$
$y = 0$ $3$
This solution is valid.
Check $y = 5$ in the original equation.
$y = 0$ $5$
$y = 0$ $6$
$y = 0$ $7$
$y = 0$ $8$
This solution is also valid.