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Simplifying 5c2 + 2 = 17c Reorder the terms: 2 + 5c2 = 17c Solving 2 + 5c2 = 17c Solving for variable 'c'. Reorder the terms: 2 + -17c + 5c2 = 17c + -17c Combine like terms: 17c + -17c = 0 2 + -17c + 5c2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -3.4c + c2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -3.4c + -0.4 + c2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -3.4c + c2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -3.4c + c2 = 0 + -0.4 -3.4c + c2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -3.4c + c2 = -0.4 The c term is -3.4c. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4c + 2.89 + c2 = -0.4 + 2.89 Reorder the terms: 2.89 + -3.4c + c2 = -0.4 + 2.89 Combine like terms: -0.4 + 2.89 = 2.49 2.89 + -3.4c + c2 = 2.49 Factor a perfect square on the left side: (c + -1.7)(c + -1.7) = 2.49 Calculate the square root of the right side: 1.577973384 Break this problem into two subproblems by setting (c + -1.7) equal to 1.577973384 and -1.577973384.Subproblem 1
c + -1.7 = 1.577973384 Simplifying c + -1.7 = 1.577973384 Reorder the terms: -1.7 + c = 1.577973384 Solving -1.7 + c = 1.577973384 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + c = 1.577973384 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + c = 1.577973384 + 1.7 c = 1.577973384 + 1.7 Combine like terms: 1.577973384 + 1.7 = 3.277973384 c = 3.277973384 Simplifying c = 3.277973384Subproblem 2
c + -1.7 = -1.577973384 Simplifying c + -1.7 = -1.577973384 Reorder the terms: -1.7 + c = -1.577973384 Solving -1.7 + c = -1.577973384 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + c = -1.577973384 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + c = -1.577973384 + 1.7 c = -1.577973384 + 1.7 Combine like terms: -1.577973384 + 1.7 = 0.122026616 c = 0.122026616 Simplifying c = 0.122026616Solution
The solution to the problem is based on the solutions from the subproblems. c = {3.277973384, 0.122026616}
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