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Simplifying -3y2 + -72y = 75 Reorder the terms: -72y + -3y2 = 75 Solving -72y + -3y2 = 75 Solving for variable 'y'. Reorder the terms: -75 + -72y + -3y2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + -72y + -3y2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(25 + 24y + y2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(25 + 24y + y2)' equal to zero and attempt to solve: Simplifying 25 + 24y + y2 = 0 Solving 25 + 24y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 24y + -25 + y2 = 0 + -25 Reorder the terms: 25 + -25 + 24y + y2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 24y + y2 = 0 + -25 24y + y2 = 0 + -25 Combine like terms: 0 + -25 = -25 24y + y2 = -25 The y term is 24y. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24y + 144 + y2 = -25 + 144 Reorder the terms: 144 + 24y + y2 = -25 + 144 Combine like terms: -25 + 144 = 119 144 + 24y + y2 = 119 Factor a perfect square on the left side: (y + 12)(y + 12) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (y + 12) equal to 10.908712115 and -10.908712115.Subproblem 1
y + 12 = 10.908712115 Simplifying y + 12 = 10.908712115 Reorder the terms: 12 + y = 10.908712115 Solving 12 + y = 10.908712115 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + y = 10.908712115 + -12 Combine like terms: 12 + -12 = 0 0 + y = 10.908712115 + -12 y = 10.908712115 + -12 Combine like terms: 10.908712115 + -12 = -1.091287885 y = -1.091287885 Simplifying y = -1.091287885Subproblem 2
y + 12 = -10.908712115 Simplifying y + 12 = -10.908712115 Reorder the terms: 12 + y = -10.908712115 Solving 12 + y = -10.908712115 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + y = -10.908712115 + -12 Combine like terms: 12 + -12 = 0 0 + y = -10.908712115 + -12 y = -10.908712115 + -12 Combine like terms: -10.908712115 + -12 = -22.908712115 y = -22.908712115 Simplifying y = -22.908712115Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.091287885, -22.908712115}Solution
y = {-1.091287885, -22.908712115}
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