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Simplifying 10c2 + -12c + 4c + -6 = 0 Reorder the terms: -6 + -12c + 4c + 10c2 = 0 Combine like terms: -12c + 4c = -8c -6 + -8c + 10c2 = 0 Solving -6 + -8c + 10c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -4c + 5c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -4c + 5c2)' equal to zero and attempt to solve: Simplifying -3 + -4c + 5c2 = 0 Solving -3 + -4c + 5c2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -0.8c + c2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.8c + 0.6 + c2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.8c + c2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.8c + c2 = 0 + 0.6 -0.8c + c2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -0.8c + c2 = 0.6 The c term is -0.8c. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8c + 0.16 + c2 = 0.6 + 0.16 Reorder the terms: 0.16 + -0.8c + c2 = 0.6 + 0.16 Combine like terms: 0.6 + 0.16 = 0.76 0.16 + -0.8c + c2 = 0.76 Factor a perfect square on the left side: (c + -0.4)(c + -0.4) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (c + -0.4) equal to 0.871779789 and -0.871779789.Subproblem 1
c + -0.4 = 0.871779789 Simplifying c + -0.4 = 0.871779789 Reorder the terms: -0.4 + c = 0.871779789 Solving -0.4 + c = 0.871779789 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + c = 0.871779789 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + c = 0.871779789 + 0.4 c = 0.871779789 + 0.4 Combine like terms: 0.871779789 + 0.4 = 1.271779789 c = 1.271779789 Simplifying c = 1.271779789Subproblem 2
c + -0.4 = -0.871779789 Simplifying c + -0.4 = -0.871779789 Reorder the terms: -0.4 + c = -0.871779789 Solving -0.4 + c = -0.871779789 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + c = -0.871779789 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + c = -0.871779789 + 0.4 c = -0.871779789 + 0.4 Combine like terms: -0.871779789 + 0.4 = -0.471779789 c = -0.471779789 Simplifying c = -0.471779789Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.271779789, -0.471779789}Solution
c = {1.271779789, -0.471779789}
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