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Simplifying c2 + -3c + -26 = 0 Reorder the terms: -26 + -3c + c2 = 0 Solving -26 + -3c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -3c + 26 + c2 = 0 + 26 Reorder the terms: -26 + 26 + -3c + c2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -3c + c2 = 0 + 26 -3c + c2 = 0 + 26 Combine like terms: 0 + 26 = 26 -3c + c2 = 26 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 + 2.25 Reorder the terms: 2.25 + -3c + c2 = 26 + 2.25 Combine like terms: 26 + 2.25 = 28.25 2.25 + -3c + c2 = 28.25 Factor a perfect square on the left side: (c + -1.5)(c + -1.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (c + -1.5) equal to 5.315072906 and -5.315072906.Subproblem 1
c + -1.5 = 5.315072906 Simplifying c + -1.5 = 5.315072906 Reorder the terms: -1.5 + c = 5.315072906 Solving -1.5 + c = 5.315072906 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 = 5.315072906 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + c = 5.315072906 + 1.5 c = 5.315072906 + 1.5 Combine like terms: 5.315072906 + 1.5 = 6.815072906 c = 6.815072906 Simplifying c = 6.815072906Subproblem 2
c + -1.5 = -5.315072906 Simplifying c + -1.5 = -5.315072906 Reorder the terms: -1.5 + c = -5.315072906 Solving -1.5 + c = -5.315072906 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 = -5.315072906 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + c = -5.315072906 + 1.5 c = -5.315072906 + 1.5 Combine like terms: -5.315072906 + 1.5 = -3.815072906 c = -3.815072906 Simplifying c = -3.815072906Solution
The solution to the problem is based on the solutions from the subproblems. c = {6.815072906, -3.815072906}
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