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Simplifying c2 + 3c = 26.2 Reorder the terms: 3c + c2 = 26.2 Solving 3c + c2 = 26.2 Solving for variable 'c'. Reorder the terms: -26.2 + 3c + c2 = 26.2 + -26.2 Combine like terms: 26.2 + -26.2 = 0.0 -26.2 + 3c + c2 = 0.0 Begin completing the square. Move the constant term to the right: Add '26.2' to each side of the equation. -26.2 + 3c + 26.2 + c2 = 0.0 + 26.2 Reorder the terms: -26.2 + 26.2 + 3c + c2 = 0.0 + 26.2 Combine like terms: -26.2 + 26.2 = 0.0 0.0 + 3c + c2 = 0.0 + 26.2 3c + c2 = 0.0 + 26.2 Combine like terms: 0.0 + 26.2 = 26.2 3c + c2 = 26.2 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 = 26.2 + 2.25 Reorder the terms: 2.25 + 3c + c2 = 26.2 + 2.25 Combine like terms: 26.2 + 2.25 = 28.45 2.25 + 3c + c2 = 28.45 Factor a perfect square on the left side: (c + 1.5)(c + 1.5) = 28.45 Calculate the square root of the right side: 5.333854141 Break this problem into two subproblems by setting (c + 1.5) equal to 5.333854141 and -5.333854141.Subproblem 1
c + 1.5 = 5.333854141 Simplifying c + 1.5 = 5.333854141 Reorder the terms: 1.5 + c = 5.333854141 Solving 1.5 + c = 5.333854141 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 = 5.333854141 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = 5.333854141 + -1.5 c = 5.333854141 + -1.5 Combine like terms: 5.333854141 + -1.5 = 3.833854141 c = 3.833854141 Simplifying c = 3.833854141Subproblem 2
c + 1.5 = -5.333854141 Simplifying c + 1.5 = -5.333854141 Reorder the terms: 1.5 + c = -5.333854141 Solving 1.5 + c = -5.333854141 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 = -5.333854141 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = -5.333854141 + -1.5 c = -5.333854141 + -1.5 Combine like terms: -5.333854141 + -1.5 = -6.833854141 c = -6.833854141 Simplifying c = -6.833854141Solution
The solution to the problem is based on the solutions from the subproblems. c = {3.833854141, -6.833854141}
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