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Simplifying 13c + c2 + -36 = 0 Reorder the terms: -36 + 13c + c2 = 0 Solving -36 + 13c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 13c + 36 + c2 = 0 + 36 Reorder the terms: -36 + 36 + 13c + c2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 13c + c2 = 0 + 36 13c + c2 = 0 + 36 Combine like terms: 0 + 36 = 36 13c + c2 = 36 The c term is 13c. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13c + 42.25 + c2 = 36 + 42.25 Reorder the terms: 42.25 + 13c + c2 = 36 + 42.25 Combine like terms: 36 + 42.25 = 78.25 42.25 + 13c + c2 = 78.25 Factor a perfect square on the left side: (c + 6.5)(c + 6.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (c + 6.5) equal to 8.845903006 and -8.845903006.Subproblem 1
c + 6.5 = 8.845903006 Simplifying c + 6.5 = 8.845903006 Reorder the terms: 6.5 + c = 8.845903006 Solving 6.5 + c = 8.845903006 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + c = 8.845903006 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + c = 8.845903006 + -6.5 c = 8.845903006 + -6.5 Combine like terms: 8.845903006 + -6.5 = 2.345903006 c = 2.345903006 Simplifying c = 2.345903006Subproblem 2
c + 6.5 = -8.845903006 Simplifying c + 6.5 = -8.845903006 Reorder the terms: 6.5 + c = -8.845903006 Solving 6.5 + c = -8.845903006 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + c = -8.845903006 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + c = -8.845903006 + -6.5 c = -8.845903006 + -6.5 Combine like terms: -8.845903006 + -6.5 = -15.345903006 c = -15.345903006 Simplifying c = -15.345903006Solution
The solution to the problem is based on the solutions from the subproblems. c = {2.345903006, -15.345903006}
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