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Simplifying 7(c + 1) * c = 4 Reorder the terms: 7(1 + c) * c = 4 Reorder the terms for easier multiplication: 7c(1 + c) = 4 (1 * 7c + c * 7c) = 4 (7c + 7c2) = 4 Solving 7c + 7c2 = 4 Solving for variable 'c'. Reorder the terms: -4 + 7c + 7c2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 7c + 7c2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + c + c2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + c + 0.5714285714 + c2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + c + c2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + c + c2 = 0 + 0.5714285714 c + c2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 c + c2 = 0.5714285714 The c term is c. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + c2 = 0.5714285714 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + c2 = 0.5714285714 + 0.25 Combine like terms: 0.5714285714 + 0.25 = 0.8214285714 1.25 + c2 = 0.8214285714 Factor a perfect square on the left side: (c + 0.5)(c + 0.5) = 0.8214285714 Calculate the square root of the right side: 0.906326967 Break this problem into two subproblems by setting (c + 0.5) equal to 0.906326967 and -0.906326967.Subproblem 1
c + 0.5 = 0.906326967 Simplifying c + 0.5 = 0.906326967 Reorder the terms: 0.5 + c = 0.906326967 Solving 0.5 + c = 0.906326967 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + c = 0.906326967 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = 0.906326967 + -0.5 c = 0.906326967 + -0.5 Combine like terms: 0.906326967 + -0.5 = 0.406326967 c = 0.406326967 Simplifying c = 0.406326967Subproblem 2
c + 0.5 = -0.906326967 Simplifying c + 0.5 = -0.906326967 Reorder the terms: 0.5 + c = -0.906326967 Solving 0.5 + c = -0.906326967 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + c = -0.906326967 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = -0.906326967 + -0.5 c = -0.906326967 + -0.5 Combine like terms: -0.906326967 + -0.5 = -1.406326967 c = -1.406326967 Simplifying c = -1.406326967Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.406326967, -1.406326967}
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