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Simplifying 4y(2 + 3y) = 48 (2 * 4y + 3y * 4y) = 48 (8y + 12y2) = 48 Solving 8y + 12y2 = 48 Solving for variable 'y'. Reorder the terms: -48 + 8y + 12y2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + 8y + 12y2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-12 + 2y + 3y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-12 + 2y + 3y2)' equal to zero and attempt to solve: Simplifying -12 + 2y + 3y2 = 0 Solving -12 + 2y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + 0.6666666667y + y2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.6666666667y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + 0.6666666667y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.6666666667y + y2 = 0 + 4 0.6666666667y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.6666666667y + y2 = 4 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 = 4 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667y + y2 = 4 + 0.1111111112 Combine like terms: 4 + 0.1111111112 = 4.1111111112 0.1111111112 + 0.6666666667y + y2 = 4.1111111112 Factor a perfect square on the left side: (y + 0.3333333334)(y + 0.3333333334) = 4.1111111112 Calculate the square root of the right side: 2.02758751 Break this problem into two subproblems by setting (y + 0.3333333334) equal to 2.02758751 and -2.02758751.Subproblem 1
y + 0.3333333334 = 2.02758751 Simplifying y + 0.3333333334 = 2.02758751 Reorder the terms: 0.3333333334 + y = 2.02758751 Solving 0.3333333334 + y = 2.02758751 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 = 2.02758751 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + y = 2.02758751 + -0.3333333334 y = 2.02758751 + -0.3333333334 Combine like terms: 2.02758751 + -0.3333333334 = 1.6942541766 y = 1.6942541766 Simplifying y = 1.6942541766Subproblem 2
y + 0.3333333334 = -2.02758751 Simplifying y + 0.3333333334 = -2.02758751 Reorder the terms: 0.3333333334 + y = -2.02758751 Solving 0.3333333334 + y = -2.02758751 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 = -2.02758751 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + y = -2.02758751 + -0.3333333334 y = -2.02758751 + -0.3333333334 Combine like terms: -2.02758751 + -0.3333333334 = -2.3609208434 y = -2.3609208434 Simplifying y = -2.3609208434Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.6942541766, -2.3609208434}Solution
y = {1.6942541766, -2.3609208434}
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