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Simplifying 6y2 + 16y + -64 = 0 Reorder the terms: -64 + 16y + 6y2 = 0 Solving -64 + 16y + 6y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-32 + 8y + 3y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-32 + 8y + 3y2)' equal to zero and attempt to solve: Simplifying -32 + 8y + 3y2 = 0 Solving -32 + 8y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10.66666667 + 2.666666667y + y2 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + 2.666666667y + 10.66666667 + y2 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + 2.666666667y + y2 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + 2.666666667y + y2 = 0 + 10.66666667 2.666666667y + y2 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 2.666666667y + y2 = 10.66666667 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 = 10.66666667 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667y + y2 = 10.66666667 + 1.777777780 Combine like terms: 10.66666667 + 1.777777780 = 12.44444445 1.777777780 + 2.666666667y + y2 = 12.44444445 Factor a perfect square on the left side: (y + 1.333333334)(y + 1.333333334) = 12.44444445 Calculate the square root of the right side: 3.527668416 Break this problem into two subproblems by setting (y + 1.333333334) equal to 3.527668416 and -3.527668416.Subproblem 1
y + 1.333333334 = 3.527668416 Simplifying y + 1.333333334 = 3.527668416 Reorder the terms: 1.333333334 + y = 3.527668416 Solving 1.333333334 + y = 3.527668416 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 = 3.527668416 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + y = 3.527668416 + -1.333333334 y = 3.527668416 + -1.333333334 Combine like terms: 3.527668416 + -1.333333334 = 2.194335082 y = 2.194335082 Simplifying y = 2.194335082Subproblem 2
y + 1.333333334 = -3.527668416 Simplifying y + 1.333333334 = -3.527668416 Reorder the terms: 1.333333334 + y = -3.527668416 Solving 1.333333334 + y = -3.527668416 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 = -3.527668416 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + y = -3.527668416 + -1.333333334 y = -3.527668416 + -1.333333334 Combine like terms: -3.527668416 + -1.333333334 = -4.86100175 y = -4.86100175 Simplifying y = -4.86100175Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.194335082, -4.86100175}Solution
y = {2.194335082, -4.86100175}
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