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Simplifying (c + -15)(c + -15) = 42 Reorder the terms: (-15 + c)(c + -15) = 42 Reorder the terms: (-15 + c)(-15 + c) = 42 Multiply (-15 + c) * (-15 + c) (-15(-15 + c) + c(-15 + c)) = 42 ((-15 * -15 + c * -15) + c(-15 + c)) = 42 ((225 + -15c) + c(-15 + c)) = 42 (225 + -15c + (-15 * c + c * c)) = 42 (225 + -15c + (-15c + c2)) = 42 Combine like terms: -15c + -15c = -30c (225 + -30c + c2) = 42 Solving 225 + -30c + c2 = 42 Solving for variable 'c'. Reorder the terms: 225 + -42 + -30c + c2 = 42 + -42 Combine like terms: 225 + -42 = 183 183 + -30c + c2 = 42 + -42 Combine like terms: 42 + -42 = 0 183 + -30c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-183' to each side of the equation. 183 + -30c + -183 + c2 = 0 + -183 Reorder the terms: 183 + -183 + -30c + c2 = 0 + -183 Combine like terms: 183 + -183 = 0 0 + -30c + c2 = 0 + -183 -30c + c2 = 0 + -183 Combine like terms: 0 + -183 = -183 -30c + c2 = -183 The c term is -30c. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30c + 225 + c2 = -183 + 225 Reorder the terms: 225 + -30c + c2 = -183 + 225 Combine like terms: -183 + 225 = 42 225 + -30c + c2 = 42 Factor a perfect square on the left side: (c + -15)(c + -15) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (c + -15) equal to 6.480740698 and -6.480740698.Subproblem 1
c + -15 = 6.480740698 Simplifying c + -15 = 6.480740698 Reorder the terms: -15 + c = 6.480740698 Solving -15 + c = 6.480740698 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + c = 6.480740698 + 15 Combine like terms: -15 + 15 = 0 0 + c = 6.480740698 + 15 c = 6.480740698 + 15 Combine like terms: 6.480740698 + 15 = 21.480740698 c = 21.480740698 Simplifying c = 21.480740698Subproblem 2
c + -15 = -6.480740698 Simplifying c + -15 = -6.480740698 Reorder the terms: -15 + c = -6.480740698 Solving -15 + c = -6.480740698 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + c = -6.480740698 + 15 Combine like terms: -15 + 15 = 0 0 + c = -6.480740698 + 15 c = -6.480740698 + 15 Combine like terms: -6.480740698 + 15 = 8.519259302 c = 8.519259302 Simplifying c = 8.519259302Solution
The solution to the problem is based on the solutions from the subproblems. c = {21.480740698, 8.519259302}
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