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Simplifying -2y2 + y = -29 Reorder the terms: y + -2y2 = -29 Solving y + -2y2 = -29 Solving for variable 'y'. Reorder the terms: 29 + y + -2y2 = -29 + 29 Combine like terms: -29 + 29 = 0 29 + y + -2y2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -14.5 + -0.5y + y2 = 0 Move the constant term to the right: Add '14.5' to each side of the equation. -14.5 + -0.5y + 14.5 + y2 = 0 + 14.5 Reorder the terms: -14.5 + 14.5 + -0.5y + y2 = 0 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + -0.5y + y2 = 0 + 14.5 -0.5y + y2 = 0 + 14.5 Combine like terms: 0 + 14.5 = 14.5 -0.5y + y2 = 14.5 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.5y + 0.25 + y2 = 14.5 + 0.25 Reorder the terms: 0.25 + -0.5y + y2 = 14.5 + 0.25 Combine like terms: 14.5 + 0.25 = 14.75 0.25 + -0.5y + y2 = 14.75 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 14.75 Calculate the square root of the right side: 3.840572874 Break this problem into two subproblems by setting (y + 0.5) equal to 3.840572874 and -3.840572874.Subproblem 1
y + 0.5 = 3.840572874 Simplifying y + 0.5 = 3.840572874 Reorder the terms: 0.5 + y = 3.840572874 Solving 0.5 + y = 3.840572874 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 3.840572874 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 3.840572874 + -0.5 y = 3.840572874 + -0.5 Combine like terms: 3.840572874 + -0.5 = 3.340572874 y = 3.340572874 Simplifying y = 3.340572874Subproblem 2
y + 0.5 = -3.840572874 Simplifying y + 0.5 = -3.840572874 Reorder the terms: 0.5 + y = -3.840572874 Solving 0.5 + y = -3.840572874 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -3.840572874 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -3.840572874 + -0.5 y = -3.840572874 + -0.5 Combine like terms: -3.840572874 + -0.5 = -4.340572874 y = -4.340572874 Simplifying y = -4.340572874Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.340572874, -4.340572874}
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