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Simplifying 6c2 + 10c = 2 Reorder the terms: 10c + 6c2 = 2 Solving 10c + 6c2 = 2 Solving for variable 'c'. Reorder the terms: -2 + 10c + 6c2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 10c + 6c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 5c + 3c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 5c + 3c2)' equal to zero and attempt to solve: Simplifying -1 + 5c + 3c2 = 0 Solving -1 + 5c + 3c2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + 1.666666667c + c2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.666666667c + 0.3333333333 + c2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.666666667c + c2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.666666667c + c2 = 0 + 0.3333333333 1.666666667c + c2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.666666667c + c2 = 0.3333333333 The c term is 1.666666667c. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667c + 0.6944444447 + c2 = 0.3333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667c + c2 = 0.3333333333 + 0.6944444447 Combine like terms: 0.3333333333 + 0.6944444447 = 1.027777778 0.6944444447 + 1.666666667c + c2 = 1.027777778 Factor a perfect square on the left side: (c + 0.8333333335)(c + 0.8333333335) = 1.027777778 Calculate the square root of the right side: 1.013793755 Break this problem into two subproblems by setting (c + 0.8333333335) equal to 1.013793755 and -1.013793755.Subproblem 1
c + 0.8333333335 = 1.013793755 Simplifying c + 0.8333333335 = 1.013793755 Reorder the terms: 0.8333333335 + c = 1.013793755 Solving 0.8333333335 + c = 1.013793755 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + c = 1.013793755 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + c = 1.013793755 + -0.8333333335 c = 1.013793755 + -0.8333333335 Combine like terms: 1.013793755 + -0.8333333335 = 0.1804604215 c = 0.1804604215 Simplifying c = 0.1804604215Subproblem 2
c + 0.8333333335 = -1.013793755 Simplifying c + 0.8333333335 = -1.013793755 Reorder the terms: 0.8333333335 + c = -1.013793755 Solving 0.8333333335 + c = -1.013793755 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + c = -1.013793755 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + c = -1.013793755 + -0.8333333335 c = -1.013793755 + -0.8333333335 Combine like terms: -1.013793755 + -0.8333333335 = -1.8471270885 c = -1.8471270885 Simplifying c = -1.8471270885Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.1804604215, -1.8471270885}Solution
c = {0.1804604215, -1.8471270885}
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