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Simplifying 10(c + 3) * c = 3 Reorder the terms: 10(3 + c) * c = 3 Reorder the terms for easier multiplication: 10c(3 + c) = 3 (3 * 10c + c * 10c) = 3 (30c + 10c2) = 3 Solving 30c + 10c2 = 3 Solving for variable 'c'. Reorder the terms: -3 + 30c + 10c2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 30c + 10c2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + 3c + c2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 3c + 0.3 + c2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 3c + c2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 3c + c2 = 0 + 0.3 3c + c2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 3c + c2 = 0.3 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 = 0.3 + 2.25 Reorder the terms: 2.25 + 3c + c2 = 0.3 + 2.25 Combine like terms: 0.3 + 2.25 = 2.55 2.25 + 3c + c2 = 2.55 Factor a perfect square on the left side: (c + 1.5)(c + 1.5) = 2.55 Calculate the square root of the right side: 1.596871942 Break this problem into two subproblems by setting (c + 1.5) equal to 1.596871942 and -1.596871942.Subproblem 1
c + 1.5 = 1.596871942 Simplifying c + 1.5 = 1.596871942 Reorder the terms: 1.5 + c = 1.596871942 Solving 1.5 + c = 1.596871942 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 = 1.596871942 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = 1.596871942 + -1.5 c = 1.596871942 + -1.5 Combine like terms: 1.596871942 + -1.5 = 0.096871942 c = 0.096871942 Simplifying c = 0.096871942Subproblem 2
c + 1.5 = -1.596871942 Simplifying c + 1.5 = -1.596871942 Reorder the terms: 1.5 + c = -1.596871942 Solving 1.5 + c = -1.596871942 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 = -1.596871942 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = -1.596871942 + -1.5 c = -1.596871942 + -1.5 Combine like terms: -1.596871942 + -1.5 = -3.096871942 c = -3.096871942 Simplifying c = -3.096871942Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.096871942, -3.096871942}
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