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Simplifying (3y + 4)(3y + 4) = 28 Reorder the terms: (4 + 3y)(3y + 4) = 28 Reorder the terms: (4 + 3y)(4 + 3y) = 28 Multiply (4 + 3y) * (4 + 3y) (4(4 + 3y) + 3y * (4 + 3y)) = 28 ((4 * 4 + 3y * 4) + 3y * (4 + 3y)) = 28 ((16 + 12y) + 3y * (4 + 3y)) = 28 (16 + 12y + (4 * 3y + 3y * 3y)) = 28 (16 + 12y + (12y + 9y2)) = 28 Combine like terms: 12y + 12y = 24y (16 + 24y + 9y2) = 28 Solving 16 + 24y + 9y2 = 28 Solving for variable 'y'. Reorder the terms: 16 + -28 + 24y + 9y2 = 28 + -28 Combine like terms: 16 + -28 = -12 -12 + 24y + 9y2 = 28 + -28 Combine like terms: 28 + -28 = 0 -12 + 24y + 9y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 8y + 3y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 8y + 3y2)' equal to zero and attempt to solve: Simplifying -4 + 8y + 3y2 = 0 Solving -4 + 8y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + 2.666666667y + y2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 2.666666667y + 1.333333333 + y2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 2.666666667y + y2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 2.666666667y + y2 = 0 + 1.333333333 2.666666667y + y2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 2.666666667y + y2 = 1.333333333 The y term is 2.666666667y. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667y + 1.777777780 + y2 = 1.333333333 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667y + y2 = 1.333333333 + 1.777777780 Combine like terms: 1.333333333 + 1.777777780 = 3.111111113 1.777777780 + 2.666666667y + y2 = 3.111111113 Factor a perfect square on the left side: (y + 1.333333334)(y + 1.333333334) = 3.111111113 Calculate the square root of the right side: 1.763834208 Break this problem into two subproblems by setting (y + 1.333333334) equal to 1.763834208 and -1.763834208.Subproblem 1
y + 1.333333334 = 1.763834208 Simplifying y + 1.333333334 = 1.763834208 Reorder the terms: 1.333333334 + y = 1.763834208 Solving 1.333333334 + y = 1.763834208 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + y = 1.763834208 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + y = 1.763834208 + -1.333333334 y = 1.763834208 + -1.333333334 Combine like terms: 1.763834208 + -1.333333334 = 0.430500874 y = 0.430500874 Simplifying y = 0.430500874Subproblem 2
y + 1.333333334 = -1.763834208 Simplifying y + 1.333333334 = -1.763834208 Reorder the terms: 1.333333334 + y = -1.763834208 Solving 1.333333334 + y = -1.763834208 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + y = -1.763834208 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + y = -1.763834208 + -1.333333334 y = -1.763834208 + -1.333333334 Combine like terms: -1.763834208 + -1.333333334 = -3.097167542 y = -3.097167542 Simplifying y = -3.097167542Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.430500874, -3.097167542}Solution
y = {0.430500874, -3.097167542}
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