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Simplifying (3y + 2)(4y) = 130 Reorder the terms: (2 + 3y)(4y) = 130 Remove parenthesis around (4y) (2 + 3y) * 4y = 130 Reorder the terms for easier multiplication: 4y(2 + 3y) = 130 (2 * 4y + 3y * 4y) = 130 (8y + 12y2) = 130 Solving 8y + 12y2 = 130 Solving for variable 'y'. Reorder the terms: -130 + 8y + 12y2 = 130 + -130 Combine like terms: 130 + -130 = 0 -130 + 8y + 12y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-65 + 4y + 6y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-65 + 4y + 6y2)' equal to zero and attempt to solve: Simplifying -65 + 4y + 6y2 = 0 Solving -65 + 4y + 6y2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -10.83333333 + 0.6666666667y + y2 = 0 Move the constant term to the right: Add '10.83333333' to each side of the equation. -10.83333333 + 0.6666666667y + 10.83333333 + y2 = 0 + 10.83333333 Reorder the terms: -10.83333333 + 10.83333333 + 0.6666666667y + y2 = 0 + 10.83333333 Combine like terms: -10.83333333 + 10.83333333 = 0.00000000 0.00000000 + 0.6666666667y + y2 = 0 + 10.83333333 0.6666666667y + y2 = 0 + 10.83333333 Combine like terms: 0 + 10.83333333 = 10.83333333 0.6666666667y + y2 = 10.83333333 The y term is 0.6666666667y. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667y + 0.1111111112 + y2 = 10.83333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667y + y2 = 10.83333333 + 0.1111111112 Combine like terms: 10.83333333 + 0.1111111112 = 10.9444444412 0.1111111112 + 0.6666666667y + y2 = 10.9444444412 Factor a perfect square on the left side: (y + 0.3333333334)(y + 0.3333333334) = 10.9444444412 Calculate the square root of the right side: 3.308238873 Break this problem into two subproblems by setting (y + 0.3333333334) equal to 3.308238873 and -3.308238873.Subproblem 1
y + 0.3333333334 = 3.308238873 Simplifying y + 0.3333333334 = 3.308238873 Reorder the terms: 0.3333333334 + y = 3.308238873 Solving 0.3333333334 + y = 3.308238873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + y = 3.308238873 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + y = 3.308238873 + -0.3333333334 y = 3.308238873 + -0.3333333334 Combine like terms: 3.308238873 + -0.3333333334 = 2.9749055396 y = 2.9749055396 Simplifying y = 2.9749055396Subproblem 2
y + 0.3333333334 = -3.308238873 Simplifying y + 0.3333333334 = -3.308238873 Reorder the terms: 0.3333333334 + y = -3.308238873 Solving 0.3333333334 + y = -3.308238873 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + y = -3.308238873 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + y = -3.308238873 + -0.3333333334 y = -3.308238873 + -0.3333333334 Combine like terms: -3.308238873 + -0.3333333334 = -3.6415722064 y = -3.6415722064 Simplifying y = -3.6415722064Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.9749055396, -3.6415722064}Solution
y = {2.9749055396, -3.6415722064}
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