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Simplifying y2 + -3y = 12 + 24 Reorder the terms: -3y + y2 = 12 + 24 Combine like terms: 12 + 24 = 36 -3y + y2 = 36 Solving -3y + y2 = 36 Solving for variable 'y'. Reorder the terms: -36 + -3y + y2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + -3y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -3y + 36 + y2 = 0 + 36 Reorder the terms: -36 + 36 + -3y + y2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -3y + y2 = 0 + 36 -3y + y2 = 0 + 36 Combine like terms: 0 + 36 = 36 -3y + y2 = 36 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 = 36 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 36 + 2.25 Combine like terms: 36 + 2.25 = 38.25 2.25 + -3y + y2 = 38.25 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (y + -1.5) equal to 6.184658438 and -6.184658438.Subproblem 1
y + -1.5 = 6.184658438 Simplifying y + -1.5 = 6.184658438 Reorder the terms: -1.5 + y = 6.184658438 Solving -1.5 + y = 6.184658438 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 = 6.184658438 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 6.184658438 + 1.5 y = 6.184658438 + 1.5 Combine like terms: 6.184658438 + 1.5 = 7.684658438 y = 7.684658438 Simplifying y = 7.684658438Subproblem 2
y + -1.5 = -6.184658438 Simplifying y + -1.5 = -6.184658438 Reorder the terms: -1.5 + y = -6.184658438 Solving -1.5 + y = -6.184658438 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 = -6.184658438 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -6.184658438 + 1.5 y = -6.184658438 + 1.5 Combine like terms: -6.184658438 + 1.5 = -4.684658438 y = -4.684658438 Simplifying y = -4.684658438Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.684658438, -4.684658438}
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