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Simplifying 4y2 + -31y + -24 = 0 Reorder the terms: -24 + -31y + 4y2 = 0 Solving -24 + -31y + 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'. -6 + -7.75y + y2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -7.75y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + -7.75y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -7.75y + y2 = 0 + 6 -7.75y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 -7.75y + y2 = 6 The y term is -7.75y. Take half its coefficient (-3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. -7.75y + 15.015625 + y2 = 6 + 15.015625 Reorder the terms: 15.015625 + -7.75y + y2 = 6 + 15.015625 Combine like terms: 6 + 15.015625 = 21.015625 15.015625 + -7.75y + y2 = 21.015625 Factor a perfect square on the left side: (y + -3.875)(y + -3.875) = 21.015625 Calculate the square root of the right side: 4.584280205 Break this problem into two subproblems by setting (y + -3.875) equal to 4.584280205 and -4.584280205.Subproblem 1
y + -3.875 = 4.584280205 Simplifying y + -3.875 = 4.584280205 Reorder the terms: -3.875 + y = 4.584280205 Solving -3.875 + y = 4.584280205 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + y = 4.584280205 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + y = 4.584280205 + 3.875 y = 4.584280205 + 3.875 Combine like terms: 4.584280205 + 3.875 = 8.459280205 y = 8.459280205 Simplifying y = 8.459280205Subproblem 2
y + -3.875 = -4.584280205 Simplifying y + -3.875 = -4.584280205 Reorder the terms: -3.875 + y = -4.584280205 Solving -3.875 + y = -4.584280205 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + y = -4.584280205 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + y = -4.584280205 + 3.875 y = -4.584280205 + 3.875 Combine like terms: -4.584280205 + 3.875 = -0.709280205 y = -0.709280205 Simplifying y = -0.709280205Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.459280205, -0.709280205}
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