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Simplifying 2y2 + -15y + -12 = 0 Reorder the terms: -12 + -15y + 2y2 = 0 Solving -12 + -15y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + -7.5y + y2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -7.5y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + -7.5y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -7.5y + y2 = 0 + 6 -7.5y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 -7.5y + y2 = 6 The y term is -7.5y. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5y + 14.0625 + y2 = 6 + 14.0625 Reorder the terms: 14.0625 + -7.5y + y2 = 6 + 14.0625 Combine like terms: 6 + 14.0625 = 20.0625 14.0625 + -7.5y + y2 = 20.0625 Factor a perfect square on the left side: (y + -3.75)(y + -3.75) = 20.0625 Calculate the square root of the right side: 4.479118217 Break this problem into two subproblems by setting (y + -3.75) equal to 4.479118217 and -4.479118217.Subproblem 1
y + -3.75 = 4.479118217 Simplifying y + -3.75 = 4.479118217 Reorder the terms: -3.75 + y = 4.479118217 Solving -3.75 + y = 4.479118217 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + y = 4.479118217 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + y = 4.479118217 + 3.75 y = 4.479118217 + 3.75 Combine like terms: 4.479118217 + 3.75 = 8.229118217 y = 8.229118217 Simplifying y = 8.229118217Subproblem 2
y + -3.75 = -4.479118217 Simplifying y + -3.75 = -4.479118217 Reorder the terms: -3.75 + y = -4.479118217 Solving -3.75 + y = -4.479118217 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + y = -4.479118217 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + y = -4.479118217 + 3.75 y = -4.479118217 + 3.75 Combine like terms: -4.479118217 + 3.75 = -0.729118217 y = -0.729118217 Simplifying y = -0.729118217Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.229118217, -0.729118217}
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