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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 = -6 -6 + -7c + c2 = 4 + -4 Combine like terms: 4 + -4 = 0 -6 + -7c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -7c + 6 + c2 = 0 + 6 Reorder the terms: -6 + 6 + -7c + c2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -7c + c2 = 0 + 6 -7c + c2 = 0 + 6 Combine like terms: 0 + 6 = 6 -7c + c2 = 6 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 = 6 + 12.25 Reorder the terms: 12.25 + -7c + c2 = 6 + 12.25 Combine like terms: 6 + 12.25 = 18.25 12.25 + -7c + c2 = 18.25 Factor a perfect square on the left side: (c + -3.5)(c + -3.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (c + -3.5) equal to 4.272001873 and -4.272001873.Subproblem 1
c + -3.5 = 4.272001873 Simplifying c + -3.5 = 4.272001873 Reorder the terms: -3.5 + c = 4.272001873 Solving -3.5 + c = 4.272001873 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 = 4.272001873 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + c = 4.272001873 + 3.5 c = 4.272001873 + 3.5 Combine like terms: 4.272001873 + 3.5 = 7.772001873 c = 7.772001873 Simplifying c = 7.772001873Subproblem 2
c + -3.5 = -4.272001873 Simplifying c + -3.5 = -4.272001873 Reorder the terms: -3.5 + c = -4.272001873 Solving -3.5 + c = -4.272001873 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 = -4.272001873 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + c = -4.272001873 + 3.5 c = -4.272001873 + 3.5 Combine like terms: -4.272001873 + 3.5 = -0.772001873 c = -0.772001873 Simplifying c = -0.772001873Solution
The solution to the problem is based on the solutions from the subproblems. c = {7.772001873, -0.772001873}
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