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Simplifying c2 + 5c + -7 = 0 Reorder the terms: -7 + 5c + c2 = 0 Solving -7 + 5c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 5c + 7 + c2 = 0 + 7 Reorder the terms: -7 + 7 + 5c + c2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 5c + c2 = 0 + 7 5c + c2 = 0 + 7 Combine like terms: 0 + 7 = 7 5c + c2 = 7 The c term is 5c. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5c + 6.25 + c2 = 7 + 6.25 Reorder the terms: 6.25 + 5c + c2 = 7 + 6.25 Combine like terms: 7 + 6.25 = 13.25 6.25 + 5c + c2 = 13.25 Factor a perfect square on the left side: (c + 2.5)(c + 2.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (c + 2.5) equal to 3.640054945 and -3.640054945.Subproblem 1
c + 2.5 = 3.640054945 Simplifying c + 2.5 = 3.640054945 Reorder the terms: 2.5 + c = 3.640054945 Solving 2.5 + c = 3.640054945 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + c = 3.640054945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + c = 3.640054945 + -2.5 c = 3.640054945 + -2.5 Combine like terms: 3.640054945 + -2.5 = 1.140054945 c = 1.140054945 Simplifying c = 1.140054945Subproblem 2
c + 2.5 = -3.640054945 Simplifying c + 2.5 = -3.640054945 Reorder the terms: 2.5 + c = -3.640054945 Solving 2.5 + c = -3.640054945 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + c = -3.640054945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + c = -3.640054945 + -2.5 c = -3.640054945 + -2.5 Combine like terms: -3.640054945 + -2.5 = -6.140054945 c = -6.140054945 Simplifying c = -6.140054945Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.140054945, -6.140054945}
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