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Simplifying 34y2 + -18y + -40 = 0 Reorder the terms: -40 + -18y + 34y2 = 0 Solving -40 + -18y + 34y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + -9y + 17y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + -9y + 17y2)' equal to zero and attempt to solve: Simplifying -20 + -9y + 17y2 = 0 Solving -20 + -9y + 17y2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -1.176470588 + -0.5294117647y + y2 = 0 Move the constant term to the right: Add '1.176470588' to each side of the equation. -1.176470588 + -0.5294117647y + 1.176470588 + y2 = 0 + 1.176470588 Reorder the terms: -1.176470588 + 1.176470588 + -0.5294117647y + y2 = 0 + 1.176470588 Combine like terms: -1.176470588 + 1.176470588 = 0.000000000 0.000000000 + -0.5294117647y + y2 = 0 + 1.176470588 -0.5294117647y + y2 = 0 + 1.176470588 Combine like terms: 0 + 1.176470588 = 1.176470588 -0.5294117647y + y2 = 1.176470588 The y term is -0.5294117647y. Take half its coefficient (-0.2647058824). Square it (0.07006920418) and add it to both sides. Add '0.07006920418' to each side of the equation. -0.5294117647y + 0.07006920418 + y2 = 1.176470588 + 0.07006920418 Reorder the terms: 0.07006920418 + -0.5294117647y + y2 = 1.176470588 + 0.07006920418 Combine like terms: 1.176470588 + 0.07006920418 = 1.24653979218 0.07006920418 + -0.5294117647y + y2 = 1.24653979218 Factor a perfect square on the left side: (y + -0.2647058824)(y + -0.2647058824) = 1.24653979218 Calculate the square root of the right side: 1.116485464 Break this problem into two subproblems by setting (y + -0.2647058824) equal to 1.116485464 and -1.116485464.Subproblem 1
y + -0.2647058824 = 1.116485464 Simplifying y + -0.2647058824 = 1.116485464 Reorder the terms: -0.2647058824 + y = 1.116485464 Solving -0.2647058824 + y = 1.116485464 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2647058824' to each side of the equation. -0.2647058824 + 0.2647058824 + y = 1.116485464 + 0.2647058824 Combine like terms: -0.2647058824 + 0.2647058824 = 0.0000000000 0.0000000000 + y = 1.116485464 + 0.2647058824 y = 1.116485464 + 0.2647058824 Combine like terms: 1.116485464 + 0.2647058824 = 1.3811913464 y = 1.3811913464 Simplifying y = 1.3811913464Subproblem 2
y + -0.2647058824 = -1.116485464 Simplifying y + -0.2647058824 = -1.116485464 Reorder the terms: -0.2647058824 + y = -1.116485464 Solving -0.2647058824 + y = -1.116485464 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2647058824' to each side of the equation. -0.2647058824 + 0.2647058824 + y = -1.116485464 + 0.2647058824 Combine like terms: -0.2647058824 + 0.2647058824 = 0.0000000000 0.0000000000 + y = -1.116485464 + 0.2647058824 y = -1.116485464 + 0.2647058824 Combine like terms: -1.116485464 + 0.2647058824 = -0.8517795816 y = -0.8517795816 Simplifying y = -0.8517795816Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.3811913464, -0.8517795816}Solution
y = {1.3811913464, -0.8517795816}
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