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Simplifying 9(c + 7) * c = 5 Reorder the terms: 9(7 + c) * c = 5 Reorder the terms for easier multiplication: 9c(7 + c) = 5 (7 * 9c + c * 9c) = 5 (63c + 9c2) = 5 Solving 63c + 9c2 = 5 Solving for variable 'c'. Reorder the terms: -5 + 63c + 9c2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 63c + 9c2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + 7c + c2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 7c + 0.5555555556 + c2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 7c + c2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 7c + c2 = 0 + 0.5555555556 7c + c2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 7c + c2 = 0.5555555556 The c term is 7c. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7c + 12.25 + c2 = 0.5555555556 + 12.25 Reorder the terms: 12.25 + 7c + c2 = 0.5555555556 + 12.25 Combine like terms: 0.5555555556 + 12.25 = 12.8055555556 12.25 + 7c + c2 = 12.8055555556 Factor a perfect square on the left side: (c + 3.5)(c + 3.5) = 12.8055555556 Calculate the square root of the right side: 3.578485092 Break this problem into two subproblems by setting (c + 3.5) equal to 3.578485092 and -3.578485092.Subproblem 1
c + 3.5 = 3.578485092 Simplifying c + 3.5 = 3.578485092 Reorder the terms: 3.5 + c = 3.578485092 Solving 3.5 + c = 3.578485092 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + c = 3.578485092 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + c = 3.578485092 + -3.5 c = 3.578485092 + -3.5 Combine like terms: 3.578485092 + -3.5 = 0.078485092 c = 0.078485092 Simplifying c = 0.078485092Subproblem 2
c + 3.5 = -3.578485092 Simplifying c + 3.5 = -3.578485092 Reorder the terms: 3.5 + c = -3.578485092 Solving 3.5 + c = -3.578485092 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + c = -3.578485092 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + c = -3.578485092 + -3.5 c = -3.578485092 + -3.5 Combine like terms: -3.578485092 + -3.5 = -7.078485092 c = -7.078485092 Simplifying c = -7.078485092Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.078485092, -7.078485092}
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