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Simplifying 5y2 + -15y + -44 = 0 Reorder the terms: -44 + -15y + 5y2 = 0 Solving -44 + -15y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8.8 + -3y + y2 = 0 Move the constant term to the right: Add '8.8' to each side of the equation. -8.8 + -3y + 8.8 + y2 = 0 + 8.8 Reorder the terms: -8.8 + 8.8 + -3y + y2 = 0 + 8.8 Combine like terms: -8.8 + 8.8 = 0.0 0.0 + -3y + y2 = 0 + 8.8 -3y + y2 = 0 + 8.8 Combine like terms: 0 + 8.8 = 8.8 -3y + y2 = 8.8 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = 8.8 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 8.8 + 2.25 Combine like terms: 8.8 + 2.25 = 11.05 2.25 + -3y + y2 = 11.05 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 11.05 Calculate the square root of the right side: 3.324154028 Break this problem into two subproblems by setting (y + -1.5) equal to 3.324154028 and -3.324154028.Subproblem 1
y + -1.5 = 3.324154028 Simplifying y + -1.5 = 3.324154028 Reorder the terms: -1.5 + y = 3.324154028 Solving -1.5 + y = 3.324154028 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 3.324154028 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 3.324154028 + 1.5 y = 3.324154028 + 1.5 Combine like terms: 3.324154028 + 1.5 = 4.824154028 y = 4.824154028 Simplifying y = 4.824154028Subproblem 2
y + -1.5 = -3.324154028 Simplifying y + -1.5 = -3.324154028 Reorder the terms: -1.5 + y = -3.324154028 Solving -1.5 + y = -3.324154028 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -3.324154028 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -3.324154028 + 1.5 y = -3.324154028 + 1.5 Combine like terms: -3.324154028 + 1.5 = -1.824154028 y = -1.824154028 Simplifying y = -1.824154028Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.824154028, -1.824154028}
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