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Simplifying 4y2 + -12y = 9 Reorder the terms: -12y + 4y2 = 9 Solving -12y + 4y2 = 9 Solving for variable 'y'. Reorder the terms: -9 + -12y + 4y2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -12y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -3y + y2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -3y + 2.25 + y2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -3y + y2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -3y + y2 = 0 + 2.25 -3y + y2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -3y + y2 = 2.25 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = 2.25 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 2.25 + 2.25 Combine like terms: 2.25 + 2.25 = 4.5 2.25 + -3y + y2 = 4.5 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (y + -1.5) equal to 2.121320344 and -2.121320344.Subproblem 1
y + -1.5 = 2.121320344 Simplifying y + -1.5 = 2.121320344 Reorder the terms: -1.5 + y = 2.121320344 Solving -1.5 + y = 2.121320344 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 2.121320344 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 2.121320344 + 1.5 y = 2.121320344 + 1.5 Combine like terms: 2.121320344 + 1.5 = 3.621320344 y = 3.621320344 Simplifying y = 3.621320344Subproblem 2
y + -1.5 = -2.121320344 Simplifying y + -1.5 = -2.121320344 Reorder the terms: -1.5 + y = -2.121320344 Solving -1.5 + y = -2.121320344 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -2.121320344 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -2.121320344 + 1.5 y = -2.121320344 + 1.5 Combine like terms: -2.121320344 + 1.5 = -0.621320344 y = -0.621320344 Simplifying y = -0.621320344Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.621320344, -0.621320344}
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