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Simplifying 4y2 + -13y + -10 = 0 Reorder the terms: -10 + -13y + 4y2 = 0 Solving -10 + -13y + 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'. -2.5 + -3.25y + y2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3.25y + 2.5 + y2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3.25y + y2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3.25y + y2 = 0 + 2.5 -3.25y + y2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3.25y + y2 = 2.5 The y term is -3.25y. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25y + 2.640625 + y2 = 2.5 + 2.640625 Reorder the terms: 2.640625 + -3.25y + y2 = 2.5 + 2.640625 Combine like terms: 2.5 + 2.640625 = 5.140625 2.640625 + -3.25y + y2 = 5.140625 Factor a perfect square on the left side: (y + -1.625)(y + -1.625) = 5.140625 Calculate the square root of the right side: 2.267294643 Break this problem into two subproblems by setting (y + -1.625) equal to 2.267294643 and -2.267294643.Subproblem 1
y + -1.625 = 2.267294643 Simplifying y + -1.625 = 2.267294643 Reorder the terms: -1.625 + y = 2.267294643 Solving -1.625 + y = 2.267294643 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + y = 2.267294643 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + y = 2.267294643 + 1.625 y = 2.267294643 + 1.625 Combine like terms: 2.267294643 + 1.625 = 3.892294643 y = 3.892294643 Simplifying y = 3.892294643Subproblem 2
y + -1.625 = -2.267294643 Simplifying y + -1.625 = -2.267294643 Reorder the terms: -1.625 + y = -2.267294643 Solving -1.625 + y = -2.267294643 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + y = -2.267294643 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + y = -2.267294643 + 1.625 y = -2.267294643 + 1.625 Combine like terms: -2.267294643 + 1.625 = -0.642294643 y = -0.642294643 Simplifying y = -0.642294643Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.892294643, -0.642294643}
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