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Simplifying 4y2 + -9y + -36 = 0 Reorder the terms: -36 + -9y + 4y2 = 0 Solving -36 + -9y + 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'. -9 + -2.25y + y2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -2.25y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + -2.25y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2.25y + y2 = 0 + 9 -2.25y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2.25y + y2 = 9 The y term is -2.25y. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25y + 1.265625 + y2 = 9 + 1.265625 Reorder the terms: 1.265625 + -2.25y + y2 = 9 + 1.265625 Combine like terms: 9 + 1.265625 = 10.265625 1.265625 + -2.25y + y2 = 10.265625 Factor a perfect square on the left side: (y + -1.125)(y + -1.125) = 10.265625 Calculate the square root of the right side: 3.204001404 Break this problem into two subproblems by setting (y + -1.125) equal to 3.204001404 and -3.204001404.Subproblem 1
y + -1.125 = 3.204001404 Simplifying y + -1.125 = 3.204001404 Reorder the terms: -1.125 + y = 3.204001404 Solving -1.125 + y = 3.204001404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + y = 3.204001404 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + y = 3.204001404 + 1.125 y = 3.204001404 + 1.125 Combine like terms: 3.204001404 + 1.125 = 4.329001404 y = 4.329001404 Simplifying y = 4.329001404Subproblem 2
y + -1.125 = -3.204001404 Simplifying y + -1.125 = -3.204001404 Reorder the terms: -1.125 + y = -3.204001404 Solving -1.125 + y = -3.204001404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + y = -3.204001404 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + y = -3.204001404 + 1.125 y = -3.204001404 + 1.125 Combine like terms: -3.204001404 + 1.125 = -2.079001404 y = -2.079001404 Simplifying y = -2.079001404Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.329001404, -2.079001404}
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