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Simplifying (c + -12) * c + -15 = 0 Reorder the terms: (-12 + c) * c + -15 = 0 Reorder the terms for easier multiplication: c(-12 + c) + -15 = 0 (-12 * c + c * c) + -15 = 0 (-12c + c2) + -15 = 0 Reorder the terms: -15 + -12c + c2 = 0 Solving -15 + -12c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -12c + 15 + c2 = 0 + 15 Reorder the terms: -15 + 15 + -12c + c2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -12c + c2 = 0 + 15 -12c + c2 = 0 + 15 Combine like terms: 0 + 15 = 15 -12c + c2 = 15 The c term is -12c. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12c + 36 + c2 = 15 + 36 Reorder the terms: 36 + -12c + c2 = 15 + 36 Combine like terms: 15 + 36 = 51 36 + -12c + c2 = 51 Factor a perfect square on the left side: (c + -6)(c + -6) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (c + -6) equal to 7.141428429 and -7.141428429.Subproblem 1
c + -6 = 7.141428429 Simplifying c + -6 = 7.141428429 Reorder the terms: -6 + c = 7.141428429 Solving -6 + c = 7.141428429 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + c = 7.141428429 + 6 Combine like terms: -6 + 6 = 0 0 + c = 7.141428429 + 6 c = 7.141428429 + 6 Combine like terms: 7.141428429 + 6 = 13.141428429 c = 13.141428429 Simplifying c = 13.141428429Subproblem 2
c + -6 = -7.141428429 Simplifying c + -6 = -7.141428429 Reorder the terms: -6 + c = -7.141428429 Solving -6 + c = -7.141428429 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + c = -7.141428429 + 6 Combine like terms: -6 + 6 = 0 0 + c = -7.141428429 + 6 c = -7.141428429 + 6 Combine like terms: -7.141428429 + 6 = -1.141428429 c = -1.141428429 Simplifying c = -1.141428429Solution
The solution to the problem is based on the solutions from the subproblems. c = {13.141428429, -1.141428429}
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