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Simplifying c2 + -6c + -25.3 = 2.5 Reorder the terms: -25.3 + -6c + c2 = 2.5 Solving -25.3 + -6c + c2 = 2.5 Solving for variable 'c'. Reorder the terms: -25.3 + -2.5 + -6c + c2 = 2.5 + -2.5 Combine like terms: -25.3 + -2.5 = -27.8 -27.8 + -6c + c2 = 2.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 -27.8 + -6c + c2 = 0.0 Begin completing the square. Move the constant term to the right: Add '27.8' to each side of the equation. -27.8 + -6c + 27.8 + c2 = 0.0 + 27.8 Reorder the terms: -27.8 + 27.8 + -6c + c2 = 0.0 + 27.8 Combine like terms: -27.8 + 27.8 = 0.0 0.0 + -6c + c2 = 0.0 + 27.8 -6c + c2 = 0.0 + 27.8 Combine like terms: 0.0 + 27.8 = 27.8 -6c + c2 = 27.8 The c term is -6c. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6c + 9 + c2 = 27.8 + 9 Reorder the terms: 9 + -6c + c2 = 27.8 + 9 Combine like terms: 27.8 + 9 = 36.8 9 + -6c + c2 = 36.8 Factor a perfect square on the left side: (c + -3)(c + -3) = 36.8 Calculate the square root of the right side: 6.066300355 Break this problem into two subproblems by setting (c + -3) equal to 6.066300355 and -6.066300355.Subproblem 1
c + -3 = 6.066300355 Simplifying c + -3 = 6.066300355 Reorder the terms: -3 + c = 6.066300355 Solving -3 + c = 6.066300355 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + c = 6.066300355 + 3 Combine like terms: -3 + 3 = 0 0 + c = 6.066300355 + 3 c = 6.066300355 + 3 Combine like terms: 6.066300355 + 3 = 9.066300355 c = 9.066300355 Simplifying c = 9.066300355Subproblem 2
c + -3 = -6.066300355 Simplifying c + -3 = -6.066300355 Reorder the terms: -3 + c = -6.066300355 Solving -3 + c = -6.066300355 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + c = -6.066300355 + 3 Combine like terms: -3 + 3 = 0 0 + c = -6.066300355 + 3 c = -6.066300355 + 3 Combine like terms: -6.066300355 + 3 = -3.066300355 c = -3.066300355 Simplifying c = -3.066300355Solution
The solution to the problem is based on the solutions from the subproblems. c = {9.066300355, -3.066300355}
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