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Simplifying y5 + -14y4 + 37y3 = 0 Reorder the terms: 37y3 + -14y4 + y5 = 0 Solving 37y3 + -14y4 + y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y3'. y3(37 + -14y + y2) = 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 '(37 + -14y + y2)' equal to zero and attempt to solve: Simplifying 37 + -14y + y2 = 0 Solving 37 + -14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + -14y + -37 + y2 = 0 + -37 Reorder the terms: 37 + -37 + -14y + y2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + -14y + y2 = 0 + -37 -14y + y2 = 0 + -37 Combine like terms: 0 + -37 = -37 -14y + y2 = -37 The y term is -14y. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14y + 49 + y2 = -37 + 49 Reorder the terms: 49 + -14y + y2 = -37 + 49 Combine like terms: -37 + 49 = 12 49 + -14y + y2 = 12 Factor a perfect square on the left side: (y + -7)(y + -7) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (y + -7) equal to 3.464101615 and -3.464101615.Subproblem 1
y + -7 = 3.464101615 Simplifying y + -7 = 3.464101615 Reorder the terms: -7 + y = 3.464101615 Solving -7 + y = 3.464101615 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = 3.464101615 + 7 Combine like terms: -7 + 7 = 0 0 + y = 3.464101615 + 7 y = 3.464101615 + 7 Combine like terms: 3.464101615 + 7 = 10.464101615 y = 10.464101615 Simplifying y = 10.464101615Subproblem 2
y + -7 = -3.464101615 Simplifying y + -7 = -3.464101615 Reorder the terms: -7 + y = -3.464101615 Solving -7 + y = -3.464101615 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = -3.464101615 + 7 Combine like terms: -7 + 7 = 0 0 + y = -3.464101615 + 7 y = -3.464101615 + 7 Combine like terms: -3.464101615 + 7 = 3.535898385 y = 3.535898385 Simplifying y = 3.535898385Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.464101615, 3.535898385}Solution
y = {10.464101615, 3.535898385}
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