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Simplifying c2 + -12c + -30 = 0 Reorder the terms: -30 + -12c + c2 = 0 Solving -30 + -12c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -12c + 30 + c2 = 0 + 30 Reorder the terms: -30 + 30 + -12c + c2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -12c + c2 = 0 + 30 -12c + c2 = 0 + 30 Combine like terms: 0 + 30 = 30 -12c + c2 = 30 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 = 30 + 36 Reorder the terms: 36 + -12c + c2 = 30 + 36 Combine like terms: 30 + 36 = 66 36 + -12c + c2 = 66 Factor a perfect square on the left side: (c + -6)(c + -6) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (c + -6) equal to 8.124038405 and -8.124038405.Subproblem 1
c + -6 = 8.124038405 Simplifying c + -6 = 8.124038405 Reorder the terms: -6 + c = 8.124038405 Solving -6 + c = 8.124038405 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 = 8.124038405 + 6 Combine like terms: -6 + 6 = 0 0 + c = 8.124038405 + 6 c = 8.124038405 + 6 Combine like terms: 8.124038405 + 6 = 14.124038405 c = 14.124038405 Simplifying c = 14.124038405Subproblem 2
c + -6 = -8.124038405 Simplifying c + -6 = -8.124038405 Reorder the terms: -6 + c = -8.124038405 Solving -6 + c = -8.124038405 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 = -8.124038405 + 6 Combine like terms: -6 + 6 = 0 0 + c = -8.124038405 + 6 c = -8.124038405 + 6 Combine like terms: -8.124038405 + 6 = -2.124038405 c = -2.124038405 Simplifying c = -2.124038405Solution
The solution to the problem is based on the solutions from the subproblems. c = {14.124038405, -2.124038405}
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