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Simplifying 49c3 + -56c2 + 77c = 0 Reorder the terms: 77c + -56c2 + 49c3 = 0 Solving 77c + -56c2 + 49c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '7c'. 7c(11 + -8c + 7c2) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'c' equal to zero and attempt to solve: Simplifying c = 0 Solving c = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c = 0Subproblem 2
Set the factor '(11 + -8c + 7c2)' equal to zero and attempt to solve: Simplifying 11 + -8c + 7c2 = 0 Solving 11 + -8c + 7c2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.571428571 + -1.142857143c + c2 = 0 Move the constant term to the right: Add '-1.571428571' to each side of the equation. 1.571428571 + -1.142857143c + -1.571428571 + c2 = 0 + -1.571428571 Reorder the terms: 1.571428571 + -1.571428571 + -1.142857143c + c2 = 0 + -1.571428571 Combine like terms: 1.571428571 + -1.571428571 = 0.000000000 0.000000000 + -1.142857143c + c2 = 0 + -1.571428571 -1.142857143c + c2 = 0 + -1.571428571 Combine like terms: 0 + -1.571428571 = -1.571428571 -1.142857143c + c2 = -1.571428571 The c term is -1.142857143c. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143c + 0.3265306123 + c2 = -1.571428571 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143c + c2 = -1.571428571 + 0.3265306123 Combine like terms: -1.571428571 + 0.3265306123 = -1.2448979587 0.3265306123 + -1.142857143c + c2 = -1.2448979587 Factor a perfect square on the left side: (c + -0.5714285715)(c + -0.5714285715) = -1.2448979587 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
c = {0}
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