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Simplifying c2 + 9c + -8 = 5 Reorder the terms: -8 + 9c + c2 = 5 Solving -8 + 9c + c2 = 5 Solving for variable 'c'. Reorder the terms: -8 + -5 + 9c + c2 = 5 + -5 Combine like terms: -8 + -5 = -13 -13 + 9c + c2 = 5 + -5 Combine like terms: 5 + -5 = 0 -13 + 9c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 9c + 13 + c2 = 0 + 13 Reorder the terms: -13 + 13 + 9c + c2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 9c + c2 = 0 + 13 9c + c2 = 0 + 13 Combine like terms: 0 + 13 = 13 9c + c2 = 13 The c term is 9c. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9c + 20.25 + c2 = 13 + 20.25 Reorder the terms: 20.25 + 9c + c2 = 13 + 20.25 Combine like terms: 13 + 20.25 = 33.25 20.25 + 9c + c2 = 33.25 Factor a perfect square on the left side: (c + 4.5)(c + 4.5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (c + 4.5) equal to 5.766281297 and -5.766281297.Subproblem 1
c + 4.5 = 5.766281297 Simplifying c + 4.5 = 5.766281297 Reorder the terms: 4.5 + c = 5.766281297 Solving 4.5 + c = 5.766281297 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + c = 5.766281297 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + c = 5.766281297 + -4.5 c = 5.766281297 + -4.5 Combine like terms: 5.766281297 + -4.5 = 1.266281297 c = 1.266281297 Simplifying c = 1.266281297Subproblem 2
c + 4.5 = -5.766281297 Simplifying c + 4.5 = -5.766281297 Reorder the terms: 4.5 + c = -5.766281297 Solving 4.5 + c = -5.766281297 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + c = -5.766281297 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + c = -5.766281297 + -4.5 c = -5.766281297 + -4.5 Combine like terms: -5.766281297 + -4.5 = -10.266281297 c = -10.266281297 Simplifying c = -10.266281297Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.266281297, -10.266281297}
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