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Simplifying 5(c + 3) * c = 3 Reorder the terms: 5(3 + c) * c = 3 Reorder the terms for easier multiplication: 5c(3 + c) = 3 (3 * 5c + c * 5c) = 3 (15c + 5c2) = 3 Solving 15c + 5c2 = 3 Solving for variable 'c'. Reorder the terms: -3 + 15c + 5c2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 15c + 5c2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + 3c + c2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 3c + 0.6 + c2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 3c + c2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 3c + c2 = 0 + 0.6 3c + c2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 3c + c2 = 0.6 The c term is 3c. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3c + 2.25 + c2 = 0.6 + 2.25 Reorder the terms: 2.25 + 3c + c2 = 0.6 + 2.25 Combine like terms: 0.6 + 2.25 = 2.85 2.25 + 3c + c2 = 2.85 Factor a perfect square on the left side: (c + 1.5)(c + 1.5) = 2.85 Calculate the square root of the right side: 1.688194302 Break this problem into two subproblems by setting (c + 1.5) equal to 1.688194302 and -1.688194302.Subproblem 1
c + 1.5 = 1.688194302 Simplifying c + 1.5 = 1.688194302 Reorder the terms: 1.5 + c = 1.688194302 Solving 1.5 + c = 1.688194302 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + c = 1.688194302 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = 1.688194302 + -1.5 c = 1.688194302 + -1.5 Combine like terms: 1.688194302 + -1.5 = 0.188194302 c = 0.188194302 Simplifying c = 0.188194302Subproblem 2
c + 1.5 = -1.688194302 Simplifying c + 1.5 = -1.688194302 Reorder the terms: 1.5 + c = -1.688194302 Solving 1.5 + c = -1.688194302 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + c = -1.688194302 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = -1.688194302 + -1.5 c = -1.688194302 + -1.5 Combine like terms: -1.688194302 + -1.5 = -3.188194302 c = -3.188194302 Simplifying c = -3.188194302Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.188194302, -3.188194302}
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