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Simplifying (4y2) + -37y + 42 = 0 Reorder the terms: 42 + -37y + (4y2) = 0 Solving 42 + -37y + (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'. 10.5 + -9.25y + y2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + -9.25y + -10.5 + y2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + -9.25y + y2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + -9.25y + y2 = 0 + -10.5 -9.25y + y2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 -9.25y + y2 = -10.5 The y term is -9.25y. Take half its coefficient (-4.625). Square it (21.390625) and add it to both sides. Add '21.390625' to each side of the equation. -9.25y + 21.390625 + y2 = -10.5 + 21.390625 Reorder the terms: 21.390625 + -9.25y + y2 = -10.5 + 21.390625 Combine like terms: -10.5 + 21.390625 = 10.890625 21.390625 + -9.25y + y2 = 10.890625 Factor a perfect square on the left side: ((y) + -4.625)((y) + -4.625) = 10.890625 Calculate the square root of the right side: 3.300094696 Break this problem into two subproblems by setting ((y) + -4.625) equal to 3.300094696 and -3.300094696.Subproblem 1
(y) + -4.625 = 3.300094696 Simplifying (y) + -4.625 = 3.300094696 y + -4.625 = 3.300094696 Reorder the terms: -4.625 + y = 3.300094696 Solving -4.625 + y = 3.300094696 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + y = 3.300094696 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + y = 3.300094696 + 4.625 y = 3.300094696 + 4.625 Combine like terms: 3.300094696 + 4.625 = 7.925094696 y = 7.925094696 Simplifying y = 7.925094696Subproblem 2
(y) + -4.625 = -3.300094696 Simplifying (y) + -4.625 = -3.300094696 y + -4.625 = -3.300094696 Reorder the terms: -4.625 + y = -3.300094696 Solving -4.625 + y = -3.300094696 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + y = -3.300094696 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + y = -3.300094696 + 4.625 y = -3.300094696 + 4.625 Combine like terms: -3.300094696 + 4.625 = 1.324905304 y = 1.324905304 Simplifying y = 1.324905304Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.925094696, 1.324905304}
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