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Simplifying c2 + -176c + 192 = 0 Reorder the terms: 192 + -176c + c2 = 0 Solving 192 + -176c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '-192' to each side of the equation. 192 + -176c + -192 + c2 = 0 + -192 Reorder the terms: 192 + -192 + -176c + c2 = 0 + -192 Combine like terms: 192 + -192 = 0 0 + -176c + c2 = 0 + -192 -176c + c2 = 0 + -192 Combine like terms: 0 + -192 = -192 -176c + c2 = -192 The c term is -176c. Take half its coefficient (-88). Square it (7744) and add it to both sides. Add '7744' to each side of the equation. -176c + 7744 + c2 = -192 + 7744 Reorder the terms: 7744 + -176c + c2 = -192 + 7744 Combine like terms: -192 + 7744 = 7552 7744 + -176c + c2 = 7552 Factor a perfect square on the left side: (c + -88)(c + -88) = 7552 Calculate the square root of the right side: 86.90224393 Break this problem into two subproblems by setting (c + -88) equal to 86.90224393 and -86.90224393.Subproblem 1
c + -88 = 86.90224393 Simplifying c + -88 = 86.90224393 Reorder the terms: -88 + c = 86.90224393 Solving -88 + c = 86.90224393 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '88' to each side of the equation. -88 + 88 + c = 86.90224393 + 88 Combine like terms: -88 + 88 = 0 0 + c = 86.90224393 + 88 c = 86.90224393 + 88 Combine like terms: 86.90224393 + 88 = 174.90224393 c = 174.90224393 Simplifying c = 174.90224393Subproblem 2
c + -88 = -86.90224393 Simplifying c + -88 = -86.90224393 Reorder the terms: -88 + c = -86.90224393 Solving -88 + c = -86.90224393 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '88' to each side of the equation. -88 + 88 + c = -86.90224393 + 88 Combine like terms: -88 + 88 = 0 0 + c = -86.90224393 + 88 c = -86.90224393 + 88 Combine like terms: -86.90224393 + 88 = 1.09775607 c = 1.09775607 Simplifying c = 1.09775607Solution
The solution to the problem is based on the solutions from the subproblems. c = {174.90224393, 1.09775607}
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