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Simplifying 8c2 + -84c + 147 = 0 Reorder the terms: 147 + -84c + 8c2 = 0 Solving 147 + -84c + 8c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 18.375 + -10.5c + c2 = 0 Move the constant term to the right: Add '-18.375' to each side of the equation. 18.375 + -10.5c + -18.375 + c2 = 0 + -18.375 Reorder the terms: 18.375 + -18.375 + -10.5c + c2 = 0 + -18.375 Combine like terms: 18.375 + -18.375 = 0.000 0.000 + -10.5c + c2 = 0 + -18.375 -10.5c + c2 = 0 + -18.375 Combine like terms: 0 + -18.375 = -18.375 -10.5c + c2 = -18.375 The c term is -10.5c. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5c + 27.5625 + c2 = -18.375 + 27.5625 Reorder the terms: 27.5625 + -10.5c + c2 = -18.375 + 27.5625 Combine like terms: -18.375 + 27.5625 = 9.1875 27.5625 + -10.5c + c2 = 9.1875 Factor a perfect square on the left side: (c + -5.25)(c + -5.25) = 9.1875 Calculate the square root of the right side: 3.031088913 Break this problem into two subproblems by setting (c + -5.25) equal to 3.031088913 and -3.031088913.Subproblem 1
c + -5.25 = 3.031088913 Simplifying c + -5.25 = 3.031088913 Reorder the terms: -5.25 + c = 3.031088913 Solving -5.25 + c = 3.031088913 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + c = 3.031088913 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + c = 3.031088913 + 5.25 c = 3.031088913 + 5.25 Combine like terms: 3.031088913 + 5.25 = 8.281088913 c = 8.281088913 Simplifying c = 8.281088913Subproblem 2
c + -5.25 = -3.031088913 Simplifying c + -5.25 = -3.031088913 Reorder the terms: -5.25 + c = -3.031088913 Solving -5.25 + c = -3.031088913 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + c = -3.031088913 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + c = -3.031088913 + 5.25 c = -3.031088913 + 5.25 Combine like terms: -3.031088913 + 5.25 = 2.218911087 c = 2.218911087 Simplifying c = 2.218911087Solution
The solution to the problem is based on the solutions from the subproblems. c = {8.281088913, 2.218911087}
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