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Simplifying (6y2 + 7y + -3) + -1(-9y + 5) = 0 Reorder the terms: (-3 + 7y + 6y2) + -1(-9y + 5) = 0 Remove parenthesis around (-3 + 7y + 6y2) -3 + 7y + 6y2 + -1(-9y + 5) = 0 Reorder the terms: -3 + 7y + 6y2 + -1(5 + -9y) = 0 -3 + 7y + 6y2 + (5 * -1 + -9y * -1) = 0 -3 + 7y + 6y2 + (-5 + 9y) = 0 Reorder the terms: -3 + -5 + 7y + 9y + 6y2 = 0 Combine like terms: -3 + -5 = -8 -8 + 7y + 9y + 6y2 = 0 Combine like terms: 7y + 9y = 16y -8 + 16y + 6y2 = 0 Solving -8 + 16y + 6y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 8y + 3y2) = 0 Ignore the factor 2.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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