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Simplifying c2 + -7c + -2 = -4 Reorder the terms: -2 + -7c + c2 = -4 Solving -2 + -7c + c2 = -4 Solving for variable 'c'. Reorder the terms: -2 + 4 + -7c + c2 = -4 + 4 Combine like terms: -2 + 4 = 2 2 + -7c + c2 = -4 + 4 Combine like terms: -4 + 4 = 0 2 + -7c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -7c + -2 + c2 = 0 + -2 Reorder the terms: 2 + -2 + -7c + c2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7c + c2 = 0 + -2 -7c + c2 = 0 + -2 Combine like terms: 0 + -2 = -2 -7c + c2 = -2 The c term is -7c. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7c + 12.25 + c2 = -2 + 12.25 Reorder the terms: 12.25 + -7c + c2 = -2 + 12.25 Combine like terms: -2 + 12.25 = 10.25 12.25 + -7c + c2 = 10.25 Factor a perfect square on the left side: (c + -3.5)(c + -3.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (c + -3.5) equal to 3.201562119 and -3.201562119.Subproblem 1
c + -3.5 = 3.201562119 Simplifying c + -3.5 = 3.201562119 Reorder the terms: -3.5 + c = 3.201562119 Solving -3.5 + c = 3.201562119 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + c = 3.201562119 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + c = 3.201562119 + 3.5 c = 3.201562119 + 3.5 Combine like terms: 3.201562119 + 3.5 = 6.701562119 c = 6.701562119 Simplifying c = 6.701562119Subproblem 2
c + -3.5 = -3.201562119 Simplifying c + -3.5 = -3.201562119 Reorder the terms: -3.5 + c = -3.201562119 Solving -3.5 + c = -3.201562119 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + c = -3.201562119 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + c = -3.201562119 + 3.5 c = -3.201562119 + 3.5 Combine like terms: -3.201562119 + 3.5 = 0.298437881 c = 0.298437881 Simplifying c = 0.298437881Solution
The solution to the problem is based on the solutions from the subproblems. c = {6.701562119, 0.298437881}
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