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Simplifying -6 + -7c(c + 10) = 0 Reorder the terms: -6 + -7c(10 + c) = 0 -6 + (10 * -7c + c * -7c) = 0 -6 + (-70c + -7c2) = 0 Solving -6 + -70c + -7c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 70c + 7c2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 70c + 7c2)' equal to zero and attempt to solve: Simplifying 6 + 70c + 7c2 = 0 Solving 6 + 70c + 7c2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.8571428571 + 10c + c2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + 10c + -0.8571428571 + c2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + 10c + c2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + 10c + c2 = 0 + -0.8571428571 10c + c2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 10c + c2 = -0.8571428571 The c term is 10c. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10c + 25 + c2 = -0.8571428571 + 25 Reorder the terms: 25 + 10c + c2 = -0.8571428571 + 25 Combine like terms: -0.8571428571 + 25 = 24.1428571429 25 + 10c + c2 = 24.1428571429 Factor a perfect square on the left side: (c + 5)(c + 5) = 24.1428571429 Calculate the square root of the right side: 4.913538149 Break this problem into two subproblems by setting (c + 5) equal to 4.913538149 and -4.913538149.Subproblem 1
c + 5 = 4.913538149 Simplifying c + 5 = 4.913538149 Reorder the terms: 5 + c = 4.913538149 Solving 5 + c = 4.913538149 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + c = 4.913538149 + -5 Combine like terms: 5 + -5 = 0 0 + c = 4.913538149 + -5 c = 4.913538149 + -5 Combine like terms: 4.913538149 + -5 = -0.086461851 c = -0.086461851 Simplifying c = -0.086461851Subproblem 2
c + 5 = -4.913538149 Simplifying c + 5 = -4.913538149 Reorder the terms: 5 + c = -4.913538149 Solving 5 + c = -4.913538149 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + c = -4.913538149 + -5 Combine like terms: 5 + -5 = 0 0 + c = -4.913538149 + -5 c = -4.913538149 + -5 Combine like terms: -4.913538149 + -5 = -9.913538149 c = -9.913538149 Simplifying c = -9.913538149Solution
The solution to the problem is based on the solutions from the subproblems. c = {-0.086461851, -9.913538149}Solution
c = {-0.086461851, -9.913538149}
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