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Simplifying 6y5 + 25y4 + 16y3 = 0 Reorder the terms: 16y3 + 25y4 + 6y5 = 0 Solving 16y3 + 25y4 + 6y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y3'. y3(16 + 25y + 6y2) = 0Subproblem 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 '(16 + 25y + 6y2)' equal to zero and attempt to solve: Simplifying 16 + 25y + 6y2 = 0 Solving 16 + 25y + 6y2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.666666667 + 4.166666667y + y2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + 4.166666667y + -2.666666667 + y2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + 4.166666667y + y2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + 4.166666667y + y2 = 0 + -2.666666667 4.166666667y + y2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 4.166666667y + y2 = -2.666666667 The y term is 4.166666667y. Take half its coefficient (2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. 4.166666667y + 4.340277781 + y2 = -2.666666667 + 4.340277781 Reorder the terms: 4.340277781 + 4.166666667y + y2 = -2.666666667 + 4.340277781 Combine like terms: -2.666666667 + 4.340277781 = 1.673611114 4.340277781 + 4.166666667y + y2 = 1.673611114 Factor a perfect square on the left side: (y + 2.083333334)(y + 2.083333334) = 1.673611114 Calculate the square root of the right side: 1.293681226 Break this problem into two subproblems by setting (y + 2.083333334) equal to 1.293681226 and -1.293681226.Subproblem 1
y + 2.083333334 = 1.293681226 Simplifying y + 2.083333334 = 1.293681226 Reorder the terms: 2.083333334 + y = 1.293681226 Solving 2.083333334 + y = 1.293681226 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + y = 1.293681226 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + y = 1.293681226 + -2.083333334 y = 1.293681226 + -2.083333334 Combine like terms: 1.293681226 + -2.083333334 = -0.789652108 y = -0.789652108 Simplifying y = -0.789652108Subproblem 2
y + 2.083333334 = -1.293681226 Simplifying y + 2.083333334 = -1.293681226 Reorder the terms: 2.083333334 + y = -1.293681226 Solving 2.083333334 + y = -1.293681226 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + y = -1.293681226 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + y = -1.293681226 + -2.083333334 y = -1.293681226 + -2.083333334 Combine like terms: -1.293681226 + -2.083333334 = -3.37701456 y = -3.37701456 Simplifying y = -3.37701456Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.789652108, -3.37701456}Solution
y = {-0.789652108, -3.37701456}
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