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Simplifying 4y2 + 27y + 10 = 0 Reorder the terms: 10 + 27y + 4y2 = 0 Solving 10 + 27y + 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 + 6.75y + y2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 6.75y + -2.5 + y2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 6.75y + y2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 6.75y + y2 = 0 + -2.5 6.75y + y2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 6.75y + y2 = -2.5 The y term is 6.75y. Take half its coefficient (3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. 6.75y + 11.390625 + y2 = -2.5 + 11.390625 Reorder the terms: 11.390625 + 6.75y + y2 = -2.5 + 11.390625 Combine like terms: -2.5 + 11.390625 = 8.890625 11.390625 + 6.75y + y2 = 8.890625 Factor a perfect square on the left side: (y + 3.375)(y + 3.375) = 8.890625 Calculate the square root of the right side: 2.98171511 Break this problem into two subproblems by setting (y + 3.375) equal to 2.98171511 and -2.98171511.Subproblem 1
y + 3.375 = 2.98171511 Simplifying y + 3.375 = 2.98171511 Reorder the terms: 3.375 + y = 2.98171511 Solving 3.375 + y = 2.98171511 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + y = 2.98171511 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + y = 2.98171511 + -3.375 y = 2.98171511 + -3.375 Combine like terms: 2.98171511 + -3.375 = -0.39328489 y = -0.39328489 Simplifying y = -0.39328489Subproblem 2
y + 3.375 = -2.98171511 Simplifying y + 3.375 = -2.98171511 Reorder the terms: 3.375 + y = -2.98171511 Solving 3.375 + y = -2.98171511 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + y = -2.98171511 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + y = -2.98171511 + -3.375 y = -2.98171511 + -3.375 Combine like terms: -2.98171511 + -3.375 = -6.35671511 y = -6.35671511 Simplifying y = -6.35671511Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.39328489, -6.35671511}
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