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Simplifying 4y2 + -34y + 38 = 0 Reorder the terms: 38 + -34y + 4y2 = 0 Solving 38 + -34y + 4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(19 + -17y + 2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + -17y + 2y2)' equal to zero and attempt to solve: Simplifying 19 + -17y + 2y2 = 0 Solving 19 + -17y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 9.5 + -8.5y + y2 = 0 Move the constant term to the right: Add '-9.5' to each side of the equation. 9.5 + -8.5y + -9.5 + y2 = 0 + -9.5 Reorder the terms: 9.5 + -9.5 + -8.5y + y2 = 0 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + -8.5y + y2 = 0 + -9.5 -8.5y + y2 = 0 + -9.5 Combine like terms: 0 + -9.5 = -9.5 -8.5y + y2 = -9.5 The y term is -8.5y. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5y + 18.0625 + y2 = -9.5 + 18.0625 Reorder the terms: 18.0625 + -8.5y + y2 = -9.5 + 18.0625 Combine like terms: -9.5 + 18.0625 = 8.5625 18.0625 + -8.5y + y2 = 8.5625 Factor a perfect square on the left side: (y + -4.25)(y + -4.25) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (y + -4.25) equal to 2.926174978 and -2.926174978.Subproblem 1
y + -4.25 = 2.926174978 Simplifying y + -4.25 = 2.926174978 Reorder the terms: -4.25 + y = 2.926174978 Solving -4.25 + y = 2.926174978 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + y = 2.926174978 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + y = 2.926174978 + 4.25 y = 2.926174978 + 4.25 Combine like terms: 2.926174978 + 4.25 = 7.176174978 y = 7.176174978 Simplifying y = 7.176174978Subproblem 2
y + -4.25 = -2.926174978 Simplifying y + -4.25 = -2.926174978 Reorder the terms: -4.25 + y = -2.926174978 Solving -4.25 + y = -2.926174978 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + y = -2.926174978 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + y = -2.926174978 + 4.25 y = -2.926174978 + 4.25 Combine like terms: -2.926174978 + 4.25 = 1.323825022 y = 1.323825022 Simplifying y = 1.323825022Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.176174978, 1.323825022}Solution
y = {7.176174978, 1.323825022}
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