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Simplifying -4y2 + 96y = -124 Reorder the terms: 96y + -4y2 = -124 Solving 96y + -4y2 = -124 Solving for variable 'y'. Reorder the terms: 124 + 96y + -4y2 = -124 + 124 Combine like terms: -124 + 124 = 0 124 + 96y + -4y2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(31 + 24y + -1y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(31 + 24y + -1y2)' equal to zero and attempt to solve: Simplifying 31 + 24y + -1y2 = 0 Solving 31 + 24y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -31 + -24y + y2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + -24y + 31 + y2 = 0 + 31 Reorder the terms: -31 + 31 + -24y + y2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -24y + y2 = 0 + 31 -24y + y2 = 0 + 31 Combine like terms: 0 + 31 = 31 -24y + y2 = 31 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 = 31 + 144 Reorder the terms: 144 + -24y + y2 = 31 + 144 Combine like terms: 31 + 144 = 175 144 + -24y + y2 = 175 Factor a perfect square on the left side: (y + -12)(y + -12) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (y + -12) equal to 13.228756555 and -13.228756555.Subproblem 1
y + -12 = 13.228756555 Simplifying y + -12 = 13.228756555 Reorder the terms: -12 + y = 13.228756555 Solving -12 + y = 13.228756555 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 = 13.228756555 + 12 Combine like terms: -12 + 12 = 0 0 + y = 13.228756555 + 12 y = 13.228756555 + 12 Combine like terms: 13.228756555 + 12 = 25.228756555 y = 25.228756555 Simplifying y = 25.228756555Subproblem 2
y + -12 = -13.228756555 Simplifying y + -12 = -13.228756555 Reorder the terms: -12 + y = -13.228756555 Solving -12 + y = -13.228756555 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 = -13.228756555 + 12 Combine like terms: -12 + 12 = 0 0 + y = -13.228756555 + 12 y = -13.228756555 + 12 Combine like terms: -13.228756555 + 12 = -1.228756555 y = -1.228756555 Simplifying y = -1.228756555Solution
The solution to the problem is based on the solutions from the subproblems. y = {25.228756555, -1.228756555}Solution
y = {25.228756555, -1.228756555}
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