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Simplifying 2y2 + -15 + -15y = y2 + -3y Reorder the terms: -15 + -15y + 2y2 = y2 + -3y Reorder the terms: -15 + -15y + 2y2 = -3y + y2 Solving -15 + -15y + 2y2 = -3y + y2 Solving for variable 'y'. Reorder the terms: -15 + -15y + 3y + 2y2 + -1y2 = -3y + y2 + 3y + -1y2 Combine like terms: -15y + 3y = -12y -15 + -12y + 2y2 + -1y2 = -3y + y2 + 3y + -1y2 Combine like terms: 2y2 + -1y2 = 1y2 -15 + -12y + 1y2 = -3y + y2 + 3y + -1y2 Reorder the terms: -15 + -12y + 1y2 = -3y + 3y + y2 + -1y2 Combine like terms: -3y + 3y = 0 -15 + -12y + 1y2 = 0 + y2 + -1y2 -15 + -12y + 1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -15 + -12y + 1y2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -12y + 15 + y2 = 0 + 15 Reorder the terms: -15 + 15 + -12y + y2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -12y + y2 = 0 + 15 -12y + y2 = 0 + 15 Combine like terms: 0 + 15 = 15 -12y + y2 = 15 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = 15 + 36 Reorder the terms: 36 + -12y + y2 = 15 + 36 Combine like terms: 15 + 36 = 51 36 + -12y + y2 = 51 Factor a perfect square on the left side: (y + -6)(y + -6) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (y + -6) equal to 7.141428429 and -7.141428429.Subproblem 1
y + -6 = 7.141428429 Simplifying y + -6 = 7.141428429 Reorder the terms: -6 + y = 7.141428429 Solving -6 + y = 7.141428429 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 7.141428429 + 6 Combine like terms: -6 + 6 = 0 0 + y = 7.141428429 + 6 y = 7.141428429 + 6 Combine like terms: 7.141428429 + 6 = 13.141428429 y = 13.141428429 Simplifying y = 13.141428429Subproblem 2
y + -6 = -7.141428429 Simplifying y + -6 = -7.141428429 Reorder the terms: -6 + y = -7.141428429 Solving -6 + y = -7.141428429 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -7.141428429 + 6 Combine like terms: -6 + 6 = 0 0 + y = -7.141428429 + 6 y = -7.141428429 + 6 Combine like terms: -7.141428429 + 6 = -1.141428429 y = -1.141428429 Simplifying y = -1.141428429Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.141428429, -1.141428429}
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