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Simplifying 4y2 + 7y + -5 = 0 Reorder the terms: -5 + 7y + 4y2 = 0 Solving -5 + 7y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 1.75y + y2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 1.75y + 1.25 + y2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 1.75y + y2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 1.75y + y2 = 0 + 1.25 1.75y + y2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 1.75y + y2 = 1.25 The y term is 1.75y. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75y + 0.765625 + y2 = 1.25 + 0.765625 Reorder the terms: 0.765625 + 1.75y + y2 = 1.25 + 0.765625 Combine like terms: 1.25 + 0.765625 = 2.015625 0.765625 + 1.75y + y2 = 2.015625 Factor a perfect square on the left side: (y + 0.875)(y + 0.875) = 2.015625 Calculate the square root of the right side: 1.419727086 Break this problem into two subproblems by setting (y + 0.875) equal to 1.419727086 and -1.419727086.Subproblem 1
y + 0.875 = 1.419727086 Simplifying y + 0.875 = 1.419727086 Reorder the terms: 0.875 + y = 1.419727086 Solving 0.875 + y = 1.419727086 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + y = 1.419727086 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + y = 1.419727086 + -0.875 y = 1.419727086 + -0.875 Combine like terms: 1.419727086 + -0.875 = 0.544727086 y = 0.544727086 Simplifying y = 0.544727086Subproblem 2
y + 0.875 = -1.419727086 Simplifying y + 0.875 = -1.419727086 Reorder the terms: 0.875 + y = -1.419727086 Solving 0.875 + y = -1.419727086 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + y = -1.419727086 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + y = -1.419727086 + -0.875 y = -1.419727086 + -0.875 Combine like terms: -1.419727086 + -0.875 = -2.294727086 y = -2.294727086 Simplifying y = -2.294727086Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.544727086, -2.294727086}
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