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Simplifying 5(c + 8) * c = 5 Reorder the terms: 5(8 + c) * c = 5 Reorder the terms for easier multiplication: 5c(8 + c) = 5 (8 * 5c + c * 5c) = 5 (40c + 5c2) = 5 Solving 40c + 5c2 = 5 Solving for variable 'c'. Reorder the terms: -5 + 40c + 5c2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 40c + 5c2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-1 + 8c + c2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + 8c + c2)' equal to zero and attempt to solve: Simplifying -1 + 8c + c2 = 0 Solving -1 + 8c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 8c + 1 + c2 = 0 + 1 Reorder the terms: -1 + 1 + 8c + c2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 8c + c2 = 0 + 1 8c + c2 = 0 + 1 Combine like terms: 0 + 1 = 1 8c + c2 = 1 The c term is 8c. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8c + 16 + c2 = 1 + 16 Reorder the terms: 16 + 8c + c2 = 1 + 16 Combine like terms: 1 + 16 = 17 16 + 8c + c2 = 17 Factor a perfect square on the left side: (c + 4)(c + 4) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (c + 4) equal to 4.123105626 and -4.123105626.Subproblem 1
c + 4 = 4.123105626 Simplifying c + 4 = 4.123105626 Reorder the terms: 4 + c = 4.123105626 Solving 4 + c = 4.123105626 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + c = 4.123105626 + -4 Combine like terms: 4 + -4 = 0 0 + c = 4.123105626 + -4 c = 4.123105626 + -4 Combine like terms: 4.123105626 + -4 = 0.123105626 c = 0.123105626 Simplifying c = 0.123105626Subproblem 2
c + 4 = -4.123105626 Simplifying c + 4 = -4.123105626 Reorder the terms: 4 + c = -4.123105626 Solving 4 + c = -4.123105626 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + c = -4.123105626 + -4 Combine like terms: 4 + -4 = 0 0 + c = -4.123105626 + -4 c = -4.123105626 + -4 Combine like terms: -4.123105626 + -4 = -8.123105626 c = -8.123105626 Simplifying c = -8.123105626Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.123105626, -8.123105626}Solution
c = {0.123105626, -8.123105626}
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