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Simplifying 7y9 + -49y6 + 7y3 = 0 Reorder the terms: 7y3 + -49y6 + 7y9 = 0 Solving 7y3 + -49y6 + 7y9 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '7y3'. 7y3(1 + -7y3 + y6) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'y3' equal to zero and attempt to solve: Simplifying y3 = 0 Solving y3 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + -7y3 + y6)' equal to zero and attempt to solve: Simplifying 1 + -7y3 + y6 = 0 Solving 1 + -7y3 + y6 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -7y3 + -1 + y6 = 0 + -1 Reorder the terms: 1 + -1 + -7y3 + y6 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7y3 + y6 = 0 + -1 -7y3 + y6 = 0 + -1 Combine like terms: 0 + -1 = -1 -7y3 + y6 = -1 The y term is -7y3. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7y3 + 12.25 + y6 = -1 + 12.25 Reorder the terms: 12.25 + -7y3 + y6 = -1 + 12.25 Combine like terms: -1 + 12.25 = 11.25 12.25 + -7y3 + y6 = 11.25 Factor a perfect square on the left side: (y3 + -3.5)(y3 + -3.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (y3 + -3.5) equal to 3.354101966 and -3.354101966.Subproblem 1
y3 + -3.5 = 3.354101966 Simplifying y3 + -3.5 = 3.354101966 Reorder the terms: -3.5 + y3 = 3.354101966 Solving -3.5 + y3 = 3.354101966 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y3 = 3.354101966 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y3 = 3.354101966 + 3.5 y3 = 3.354101966 + 3.5 Combine like terms: 3.354101966 + 3.5 = 6.854101966 y3 = 6.854101966 Simplifying y3 = 6.854101966 Reorder the terms: -6.854101966 + y3 = 6.854101966 + -6.854101966 Combine like terms: 6.854101966 + -6.854101966 = 0.000000000 -6.854101966 + y3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
y3 + -3.5 = -3.354101966 Simplifying y3 + -3.5 = -3.354101966 Reorder the terms: -3.5 + y3 = -3.354101966 Solving -3.5 + y3 = -3.354101966 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y3 = -3.354101966 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y3 = -3.354101966 + 3.5 y3 = -3.354101966 + 3.5 Combine like terms: -3.354101966 + 3.5 = 0.145898034 y3 = 0.145898034 Simplifying y3 = 0.145898034 Reorder the terms: -0.145898034 + y3 = 0.145898034 + -0.145898034 Combine like terms: 0.145898034 + -0.145898034 = 0.000000000 -0.145898034 + y3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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