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Simplifying 26c2 + 108c + 108 = 0 Reorder the terms: 108 + 108c + 26c2 = 0 Solving 108 + 108c + 26c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(54 + 54c + 13c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(54 + 54c + 13c2)' equal to zero and attempt to solve: Simplifying 54 + 54c + 13c2 = 0 Solving 54 + 54c + 13c2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 4.153846154 + 4.153846154c + c2 = 0 Move the constant term to the right: Add '-4.153846154' to each side of the equation. 4.153846154 + 4.153846154c + -4.153846154 + c2 = 0 + -4.153846154 Reorder the terms: 4.153846154 + -4.153846154 + 4.153846154c + c2 = 0 + -4.153846154 Combine like terms: 4.153846154 + -4.153846154 = 0.000000000 0.000000000 + 4.153846154c + c2 = 0 + -4.153846154 4.153846154c + c2 = 0 + -4.153846154 Combine like terms: 0 + -4.153846154 = -4.153846154 4.153846154c + c2 = -4.153846154 The c term is 4.153846154c. Take half its coefficient (2.076923077). Square it (4.313609468) and add it to both sides. Add '4.313609468' to each side of the equation. 4.153846154c + 4.313609468 + c2 = -4.153846154 + 4.313609468 Reorder the terms: 4.313609468 + 4.153846154c + c2 = -4.153846154 + 4.313609468 Combine like terms: -4.153846154 + 4.313609468 = 0.159763314 4.313609468 + 4.153846154c + c2 = 0.159763314 Factor a perfect square on the left side: (c + 2.076923077)(c + 2.076923077) = 0.159763314 Calculate the square root of the right side: 0.399704033 Break this problem into two subproblems by setting (c + 2.076923077) equal to 0.399704033 and -0.399704033.Subproblem 1
c + 2.076923077 = 0.399704033 Simplifying c + 2.076923077 = 0.399704033 Reorder the terms: 2.076923077 + c = 0.399704033 Solving 2.076923077 + c = 0.399704033 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.076923077' to each side of the equation. 2.076923077 + -2.076923077 + c = 0.399704033 + -2.076923077 Combine like terms: 2.076923077 + -2.076923077 = 0.000000000 0.000000000 + c = 0.399704033 + -2.076923077 c = 0.399704033 + -2.076923077 Combine like terms: 0.399704033 + -2.076923077 = -1.677219044 c = -1.677219044 Simplifying c = -1.677219044Subproblem 2
c + 2.076923077 = -0.399704033 Simplifying c + 2.076923077 = -0.399704033 Reorder the terms: 2.076923077 + c = -0.399704033 Solving 2.076923077 + c = -0.399704033 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.076923077' to each side of the equation. 2.076923077 + -2.076923077 + c = -0.399704033 + -2.076923077 Combine like terms: 2.076923077 + -2.076923077 = 0.000000000 0.000000000 + c = -0.399704033 + -2.076923077 c = -0.399704033 + -2.076923077 Combine like terms: -0.399704033 + -2.076923077 = -2.47662711 c = -2.47662711 Simplifying c = -2.47662711Solution
The solution to the problem is based on the solutions from the subproblems. c = {-1.677219044, -2.47662711}Solution
c = {-1.677219044, -2.47662711}
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