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Simplifying -4y2 + 23y + 15 = 0 Reorder the terms: 15 + 23y + -4y2 = 0 Solving 15 + 23y + -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'. -3.75 + -5.75y + y2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -5.75y + 3.75 + y2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -5.75y + y2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -5.75y + y2 = 0 + 3.75 -5.75y + y2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -5.75y + y2 = 3.75 The y term is -5.75y. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75y + 8.265625 + y2 = 3.75 + 8.265625 Reorder the terms: 8.265625 + -5.75y + y2 = 3.75 + 8.265625 Combine like terms: 3.75 + 8.265625 = 12.015625 8.265625 + -5.75y + y2 = 12.015625 Factor a perfect square on the left side: (y + -2.875)(y + -2.875) = 12.015625 Calculate the square root of the right side: 3.466356156 Break this problem into two subproblems by setting (y + -2.875) equal to 3.466356156 and -3.466356156.Subproblem 1
y + -2.875 = 3.466356156 Simplifying y + -2.875 = 3.466356156 Reorder the terms: -2.875 + y = 3.466356156 Solving -2.875 + y = 3.466356156 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + y = 3.466356156 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + y = 3.466356156 + 2.875 y = 3.466356156 + 2.875 Combine like terms: 3.466356156 + 2.875 = 6.341356156 y = 6.341356156 Simplifying y = 6.341356156Subproblem 2
y + -2.875 = -3.466356156 Simplifying y + -2.875 = -3.466356156 Reorder the terms: -2.875 + y = -3.466356156 Solving -2.875 + y = -3.466356156 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + y = -3.466356156 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + y = -3.466356156 + 2.875 y = -3.466356156 + 2.875 Combine like terms: -3.466356156 + 2.875 = -0.591356156 y = -0.591356156 Simplifying y = -0.591356156Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.341356156, -0.591356156}
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