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Simplifying c2 + 6c + -49 = 0 Reorder the terms: -49 + 6c + c2 = 0 Solving -49 + 6c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 6c + 49 + c2 = 0 + 49 Reorder the terms: -49 + 49 + 6c + c2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 6c + c2 = 0 + 49 6c + c2 = 0 + 49 Combine like terms: 0 + 49 = 49 6c + c2 = 49 The c term is 6c. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6c + 9 + c2 = 49 + 9 Reorder the terms: 9 + 6c + c2 = 49 + 9 Combine like terms: 49 + 9 = 58 9 + 6c + c2 = 58 Factor a perfect square on the left side: (c + 3)(c + 3) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (c + 3) equal to 7.615773106 and -7.615773106.Subproblem 1
c + 3 = 7.615773106 Simplifying c + 3 = 7.615773106 Reorder the terms: 3 + c = 7.615773106 Solving 3 + c = 7.615773106 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + c = 7.615773106 + -3 Combine like terms: 3 + -3 = 0 0 + c = 7.615773106 + -3 c = 7.615773106 + -3 Combine like terms: 7.615773106 + -3 = 4.615773106 c = 4.615773106 Simplifying c = 4.615773106Subproblem 2
c + 3 = -7.615773106 Simplifying c + 3 = -7.615773106 Reorder the terms: 3 + c = -7.615773106 Solving 3 + c = -7.615773106 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + c = -7.615773106 + -3 Combine like terms: 3 + -3 = 0 0 + c = -7.615773106 + -3 c = -7.615773106 + -3 Combine like terms: -7.615773106 + -3 = -10.615773106 c = -10.615773106 Simplifying c = -10.615773106Solution
The solution to the problem is based on the solutions from the subproblems. c = {4.615773106, -10.615773106}
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