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Simplifying -9 + 2.5y + -0.7y + 1 + 6.4y2 = 0 Reorder the terms: -9 + 1 + 2.5y + -0.7y + 6.4y2 = 0 Combine like terms: -9 + 1 = -8 -8 + 2.5y + -0.7y + 6.4y2 = 0 Combine like terms: 2.5y + -0.7y = 1.8y -8 + 1.8y + 6.4y2 = 0 Solving -8 + 1.8y + 6.4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 6.4 the coefficient of the squared term: Divide each side by '6.4'. -1.25 + 0.28125y + y2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 0.28125y + 1.25 + y2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 0.28125y + y2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 0.28125y + y2 = 0 + 1.25 0.28125y + y2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 0.28125y + y2 = 1.25 The y term is 0.28125y. Take half its coefficient (0.140625). Square it (0.01977539063) and add it to both sides. Add '0.01977539063' to each side of the equation. 0.28125y + 0.01977539063 + y2 = 1.25 + 0.01977539063 Reorder the terms: 0.01977539063 + 0.28125y + y2 = 1.25 + 0.01977539063 Combine like terms: 1.25 + 0.01977539063 = 1.26977539063 0.01977539063 + 0.28125y + y2 = 1.26977539063 Factor a perfect square on the left side: (y + 0.140625)(y + 0.140625) = 1.26977539063 Calculate the square root of the right side: 1.126843108 Break this problem into two subproblems by setting (y + 0.140625) equal to 1.126843108 and -1.126843108.Subproblem 1
y + 0.140625 = 1.126843108 Simplifying y + 0.140625 = 1.126843108 Reorder the terms: 0.140625 + y = 1.126843108 Solving 0.140625 + y = 1.126843108 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.140625' to each side of the equation. 0.140625 + -0.140625 + y = 1.126843108 + -0.140625 Combine like terms: 0.140625 + -0.140625 = 0.000000 0.000000 + y = 1.126843108 + -0.140625 y = 1.126843108 + -0.140625 Combine like terms: 1.126843108 + -0.140625 = 0.986218108 y = 0.986218108 Simplifying y = 0.986218108Subproblem 2
y + 0.140625 = -1.126843108 Simplifying y + 0.140625 = -1.126843108 Reorder the terms: 0.140625 + y = -1.126843108 Solving 0.140625 + y = -1.126843108 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.140625' to each side of the equation. 0.140625 + -0.140625 + y = -1.126843108 + -0.140625 Combine like terms: 0.140625 + -0.140625 = 0.000000 0.000000 + y = -1.126843108 + -0.140625 y = -1.126843108 + -0.140625 Combine like terms: -1.126843108 + -0.140625 = -1.267468108 y = -1.267468108 Simplifying y = -1.267468108Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.986218108, -1.267468108}
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