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Simplifying (c4) + -1(4c2) + 1 = 0 c4 + -1(4c2) + 1 = 0 Remove parenthesis around (4c2) c4 + -1 * 4c2 + 1 = 0 Multiply -1 * 4 c4 + -4c2 + 1 = 0 Reorder the terms: 1 + -4c2 + c4 = 0 Solving 1 + -4c2 + c4 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4c2 + -1 + c4 = 0 + -1 Reorder the terms: 1 + -1 + -4c2 + c4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4c2 + c4 = 0 + -1 -4c2 + c4 = 0 + -1 Combine like terms: 0 + -1 = -1 -4c2 + c4 = -1 The c term is -4c2. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4c2 + 4 + c4 = -1 + 4 Reorder the terms: 4 + -4c2 + c4 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + -4c2 + c4 = 3 Factor a perfect square on the left side: (c2 + -2)(c2 + -2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (c2 + -2) equal to 1.732050808 and -1.732050808.Subproblem 1
c2 + -2 = 1.732050808 Simplifying c2 + -2 = 1.732050808 Reorder the terms: -2 + c2 = 1.732050808 Solving -2 + c2 = 1.732050808 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + c2 = 1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + c2 = 1.732050808 + 2 c2 = 1.732050808 + 2 Combine like terms: 1.732050808 + 2 = 3.732050808 c2 = 3.732050808 Simplifying c2 = 3.732050808 Take the square root of each side: c = {-1.931851653, 1.931851653}Subproblem 2
c2 + -2 = -1.732050808 Simplifying c2 + -2 = -1.732050808 Reorder the terms: -2 + c2 = -1.732050808 Solving -2 + c2 = -1.732050808 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + c2 = -1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + c2 = -1.732050808 + 2 c2 = -1.732050808 + 2 Combine like terms: -1.732050808 + 2 = 0.267949192 c2 = 0.267949192 Simplifying c2 = 0.267949192 Take the square root of each side: c = {-0.51763809, 0.51763809}Solution
The solution to the problem is based on the solutions from the subproblems. c = {-1.931851653, 1.931851653, -0.51763809, 0.51763809}
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