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Simplifying 9y2 + -42y + -49 = 50 Reorder the terms: -49 + -42y + 9y2 = 50 Solving -49 + -42y + 9y2 = 50 Solving for variable 'y'. Reorder the terms: -49 + -50 + -42y + 9y2 = 50 + -50 Combine like terms: -49 + -50 = -99 -99 + -42y + 9y2 = 50 + -50 Combine like terms: 50 + -50 = 0 -99 + -42y + 9y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-33 + -14y + 3y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-33 + -14y + 3y2)' equal to zero and attempt to solve: Simplifying -33 + -14y + 3y2 = 0 Solving -33 + -14y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -11 + -4.666666667y + y2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -4.666666667y + 11 + y2 = 0 + 11 Reorder the terms: -11 + 11 + -4.666666667y + y2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -4.666666667y + y2 = 0 + 11 -4.666666667y + y2 = 0 + 11 Combine like terms: 0 + 11 = 11 -4.666666667y + y2 = 11 The y term is -4.666666667y. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667y + 5.444444448 + y2 = 11 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667y + y2 = 11 + 5.444444448 Combine like terms: 11 + 5.444444448 = 16.444444448 5.444444448 + -4.666666667y + y2 = 16.444444448 Factor a perfect square on the left side: (y + -2.333333334)(y + -2.333333334) = 16.444444448 Calculate the square root of the right side: 4.055175021 Break this problem into two subproblems by setting (y + -2.333333334) equal to 4.055175021 and -4.055175021.Subproblem 1
y + -2.333333334 = 4.055175021 Simplifying y + -2.333333334 = 4.055175021 Reorder the terms: -2.333333334 + y = 4.055175021 Solving -2.333333334 + y = 4.055175021 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + y = 4.055175021 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + y = 4.055175021 + 2.333333334 y = 4.055175021 + 2.333333334 Combine like terms: 4.055175021 + 2.333333334 = 6.388508355 y = 6.388508355 Simplifying y = 6.388508355Subproblem 2
y + -2.333333334 = -4.055175021 Simplifying y + -2.333333334 = -4.055175021 Reorder the terms: -2.333333334 + y = -4.055175021 Solving -2.333333334 + y = -4.055175021 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + y = -4.055175021 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + y = -4.055175021 + 2.333333334 y = -4.055175021 + 2.333333334 Combine like terms: -4.055175021 + 2.333333334 = -1.721841687 y = -1.721841687 Simplifying y = -1.721841687Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.388508355, -1.721841687}Solution
y = {6.388508355, -1.721841687}
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