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Simplifying c2 + -12c = 38 Reorder the terms: -12c + c2 = 38 Solving -12c + c2 = 38 Solving for variable 'c'. Reorder the terms: -38 + -12c + c2 = 38 + -38 Combine like terms: 38 + -38 = 0 -38 + -12c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + -12c + 38 + c2 = 0 + 38 Reorder the terms: -38 + 38 + -12c + c2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -12c + c2 = 0 + 38 -12c + c2 = 0 + 38 Combine like terms: 0 + 38 = 38 -12c + c2 = 38 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 = 38 + 36 Reorder the terms: 36 + -12c + c2 = 38 + 36 Combine like terms: 38 + 36 = 74 36 + -12c + c2 = 74 Factor a perfect square on the left side: (c + -6)(c + -6) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (c + -6) equal to 8.602325267 and -8.602325267.Subproblem 1
c + -6 = 8.602325267 Simplifying c + -6 = 8.602325267 Reorder the terms: -6 + c = 8.602325267 Solving -6 + c = 8.602325267 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 = 8.602325267 + 6 Combine like terms: -6 + 6 = 0 0 + c = 8.602325267 + 6 c = 8.602325267 + 6 Combine like terms: 8.602325267 + 6 = 14.602325267 c = 14.602325267 Simplifying c = 14.602325267Subproblem 2
c + -6 = -8.602325267 Simplifying c + -6 = -8.602325267 Reorder the terms: -6 + c = -8.602325267 Solving -6 + c = -8.602325267 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 = -8.602325267 + 6 Combine like terms: -6 + 6 = 0 0 + c = -8.602325267 + 6 c = -8.602325267 + 6 Combine like terms: -8.602325267 + 6 = -2.602325267 c = -2.602325267 Simplifying c = -2.602325267Solution
The solution to the problem is based on the solutions from the subproblems. c = {14.602325267, -2.602325267}
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