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Simplifying 10(c + 9) * c = 3 Reorder the terms: 10(9 + c) * c = 3 Reorder the terms for easier multiplication: 10c(9 + c) = 3 (9 * 10c + c * 10c) = 3 (90c + 10c2) = 3 Solving 90c + 10c2 = 3 Solving for variable 'c'. Reorder the terms: -3 + 90c + 10c2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 90c + 10c2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + 9c + c2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 9c + 0.3 + c2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 9c + c2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 9c + c2 = 0 + 0.3 9c + c2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 9c + c2 = 0.3 The c term is 9c. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9c + 20.25 + c2 = 0.3 + 20.25 Reorder the terms: 20.25 + 9c + c2 = 0.3 + 20.25 Combine like terms: 0.3 + 20.25 = 20.55 20.25 + 9c + c2 = 20.55 Factor a perfect square on the left side: (c + 4.5)(c + 4.5) = 20.55 Calculate the square root of the right side: 4.533210783 Break this problem into two subproblems by setting (c + 4.5) equal to 4.533210783 and -4.533210783.Subproblem 1
c + 4.5 = 4.533210783 Simplifying c + 4.5 = 4.533210783 Reorder the terms: 4.5 + c = 4.533210783 Solving 4.5 + c = 4.533210783 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + c = 4.533210783 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + c = 4.533210783 + -4.5 c = 4.533210783 + -4.5 Combine like terms: 4.533210783 + -4.5 = 0.033210783 c = 0.033210783 Simplifying c = 0.033210783Subproblem 2
c + 4.5 = -4.533210783 Simplifying c + 4.5 = -4.533210783 Reorder the terms: 4.5 + c = -4.533210783 Solving 4.5 + c = -4.533210783 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + c = -4.533210783 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + c = -4.533210783 + -4.5 c = -4.533210783 + -4.5 Combine like terms: -4.533210783 + -4.5 = -9.033210783 c = -9.033210783 Simplifying c = -9.033210783Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.033210783, -9.033210783}
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