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Simplifying -3y2 + -48y + -129 = 0 Reorder the terms: -129 + -48y + -3y2 = 0 Solving -129 + -48y + -3y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-3'. -3(43 + 16y + y2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(43 + 16y + y2)' equal to zero and attempt to solve: Simplifying 43 + 16y + y2 = 0 Solving 43 + 16y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + 16y + -43 + y2 = 0 + -43 Reorder the terms: 43 + -43 + 16y + y2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 16y + y2 = 0 + -43 16y + y2 = 0 + -43 Combine like terms: 0 + -43 = -43 16y + y2 = -43 The y term is 16y. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16y + 64 + y2 = -43 + 64 Reorder the terms: 64 + 16y + y2 = -43 + 64 Combine like terms: -43 + 64 = 21 64 + 16y + y2 = 21 Factor a perfect square on the left side: (y + 8)(y + 8) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (y + 8) equal to 4.582575695 and -4.582575695.Subproblem 1
y + 8 = 4.582575695 Simplifying y + 8 = 4.582575695 Reorder the terms: 8 + y = 4.582575695 Solving 8 + y = 4.582575695 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + y = 4.582575695 + -8 Combine like terms: 8 + -8 = 0 0 + y = 4.582575695 + -8 y = 4.582575695 + -8 Combine like terms: 4.582575695 + -8 = -3.417424305 y = -3.417424305 Simplifying y = -3.417424305Subproblem 2
y + 8 = -4.582575695 Simplifying y + 8 = -4.582575695 Reorder the terms: 8 + y = -4.582575695 Solving 8 + y = -4.582575695 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + y = -4.582575695 + -8 Combine like terms: 8 + -8 = 0 0 + y = -4.582575695 + -8 y = -4.582575695 + -8 Combine like terms: -4.582575695 + -8 = -12.582575695 y = -12.582575695 Simplifying y = -12.582575695Solution
The solution to the problem is based on the solutions from the subproblems. y = {-3.417424305, -12.582575695}Solution
y = {-3.417424305, -12.582575695}
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