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Simplifying (7c3 + -5c2 + 2c) + -1(-3c3 + 2c2 + -1c) = 0 Reorder the terms: (2c + -5c2 + 7c3) + -1(-3c3 + 2c2 + -1c) = 0 Remove parenthesis around (2c + -5c2 + 7c3) 2c + -5c2 + 7c3 + -1(-3c3 + 2c2 + -1c) = 0 Reorder the terms: 2c + -5c2 + 7c3 + -1(-1c + 2c2 + -3c3) = 0 2c + -5c2 + 7c3 + (-1c * -1 + 2c2 * -1 + -3c3 * -1) = 0 2c + -5c2 + 7c3 + (1c + -2c2 + 3c3) = 0 Reorder the terms: 2c + 1c + -5c2 + -2c2 + 7c3 + 3c3 = 0 Combine like terms: 2c + 1c = 3c 3c + -5c2 + -2c2 + 7c3 + 3c3 = 0 Combine like terms: -5c2 + -2c2 = -7c2 3c + -7c2 + 7c3 + 3c3 = 0 Combine like terms: 7c3 + 3c3 = 10c3 3c + -7c2 + 10c3 = 0 Solving 3c + -7c2 + 10c3 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), 'c'. c(3 + -7c + 10c2) = 0Subproblem 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 '(3 + -7c + 10c2)' equal to zero and attempt to solve: Simplifying 3 + -7c + 10c2 = 0 Solving 3 + -7c + 10c2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.3 + -0.7c + c2 = 0.0 Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + -0.7c + -0.3 + c2 = 0.0 + -0.3 Reorder the terms: 0.3 + -0.3 + -0.7c + c2 = 0.0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + -0.7c + c2 = 0.0 + -0.3 -0.7c + c2 = 0.0 + -0.3 Combine like terms: 0.0 + -0.3 = -0.3 -0.7c + c2 = -0.3 The c term is -0.7c. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7c + 0.1225 + c2 = -0.3 + 0.1225 Reorder the terms: 0.1225 + -0.7c + c2 = -0.3 + 0.1225 Combine like terms: -0.3 + 0.1225 = -0.1775 0.1225 + -0.7c + c2 = -0.1775 Factor a perfect square on the left side: (c + -0.35)(c + -0.35) = -0.1775 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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