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Simplifying y = 3y2 + 28y + 49 Reorder the terms: y = 49 + 28y + 3y2 Solving y = 49 + 28y + 3y2 Solving for variable 'y'. Reorder the terms: -49 + y + -28y + -3y2 = 49 + 28y + 3y2 + -49 + -28y + -3y2 Combine like terms: y + -28y = -27y -49 + -27y + -3y2 = 49 + 28y + 3y2 + -49 + -28y + -3y2 Reorder the terms: -49 + -27y + -3y2 = 49 + -49 + 28y + -28y + 3y2 + -3y2 Combine like terms: 49 + -49 = 0 -49 + -27y + -3y2 = 0 + 28y + -28y + 3y2 + -3y2 -49 + -27y + -3y2 = 28y + -28y + 3y2 + -3y2 Combine like terms: 28y + -28y = 0 -49 + -27y + -3y2 = 0 + 3y2 + -3y2 -49 + -27y + -3y2 = 3y2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 -49 + -27y + -3y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(49 + 27y + 3y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(49 + 27y + 3y2)' equal to zero and attempt to solve: Simplifying 49 + 27y + 3y2 = 0 Solving 49 + 27y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 16.33333333 + 9y + y2 = 0 Move the constant term to the right: Add '-16.33333333' to each side of the equation. 16.33333333 + 9y + -16.33333333 + y2 = 0 + -16.33333333 Reorder the terms: 16.33333333 + -16.33333333 + 9y + y2 = 0 + -16.33333333 Combine like terms: 16.33333333 + -16.33333333 = 0.00000000 0.00000000 + 9y + y2 = 0 + -16.33333333 9y + y2 = 0 + -16.33333333 Combine like terms: 0 + -16.33333333 = -16.33333333 9y + y2 = -16.33333333 The y term is 9y. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9y + 20.25 + y2 = -16.33333333 + 20.25 Reorder the terms: 20.25 + 9y + y2 = -16.33333333 + 20.25 Combine like terms: -16.33333333 + 20.25 = 3.91666667 20.25 + 9y + y2 = 3.91666667 Factor a perfect square on the left side: (y + 4.5)(y + 4.5) = 3.91666667 Calculate the square root of the right side: 1.979057015 Break this problem into two subproblems by setting (y + 4.5) equal to 1.979057015 and -1.979057015.Subproblem 1
y + 4.5 = 1.979057015 Simplifying y + 4.5 = 1.979057015 Reorder the terms: 4.5 + y = 1.979057015 Solving 4.5 + y = 1.979057015 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + y = 1.979057015 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = 1.979057015 + -4.5 y = 1.979057015 + -4.5 Combine like terms: 1.979057015 + -4.5 = -2.520942985 y = -2.520942985 Simplifying y = -2.520942985Subproblem 2
y + 4.5 = -1.979057015 Simplifying y + 4.5 = -1.979057015 Reorder the terms: 4.5 + y = -1.979057015 Solving 4.5 + y = -1.979057015 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + y = -1.979057015 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = -1.979057015 + -4.5 y = -1.979057015 + -4.5 Combine like terms: -1.979057015 + -4.5 = -6.479057015 y = -6.479057015 Simplifying y = -6.479057015Solution
The solution to the problem is based on the solutions from the subproblems. y = {-2.520942985, -6.479057015}Solution
y = {-2.520942985, -6.479057015}
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