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Simplifying -4y2 + -1y = -10 Reorder the terms: -1y + -4y2 = -10 Solving -1y + -4y2 = -10 Solving for variable 'y'. Reorder the terms: 10 + -1y + -4y2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + -1y + -4y2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.5 + 0.25y + y2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 0.25y + 2.5 + y2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 0.25y + y2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 0.25y + y2 = 0 + 2.5 0.25y + y2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 0.25y + y2 = 2.5 The y term is 0.25y. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25y + 0.015625 + y2 = 2.5 + 0.015625 Reorder the terms: 0.015625 + 0.25y + y2 = 2.5 + 0.015625 Combine like terms: 2.5 + 0.015625 = 2.515625 0.015625 + 0.25y + y2 = 2.515625 Factor a perfect square on the left side: (y + 0.125)(y + 0.125) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (y + 0.125) equal to 1.586072193 and -1.586072193.Subproblem 1
y + 0.125 = 1.586072193 Simplifying y + 0.125 = 1.586072193 Reorder the terms: 0.125 + y = 1.586072193 Solving 0.125 + y = 1.586072193 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + y = 1.586072193 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + y = 1.586072193 + -0.125 y = 1.586072193 + -0.125 Combine like terms: 1.586072193 + -0.125 = 1.461072193 y = 1.461072193 Simplifying y = 1.461072193Subproblem 2
y + 0.125 = -1.586072193 Simplifying y + 0.125 = -1.586072193 Reorder the terms: 0.125 + y = -1.586072193 Solving 0.125 + y = -1.586072193 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + y = -1.586072193 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + y = -1.586072193 + -0.125 y = -1.586072193 + -0.125 Combine like terms: -1.586072193 + -0.125 = -1.711072193 y = -1.711072193 Simplifying y = -1.711072193Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.461072193, -1.711072193}
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