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Simplifying (c + 0.5)(c + 0.5) = 0 Reorder the terms: (0.5 + c)(c + 0.5) = 0 Reorder the terms: (0.5 + c)(0.5 + c) = 0 Multiply (0.5 + c) * (0.5 + c) (0.5(0.5 + c) + c(0.5 + c)) = 0 ((0.5 * 0.5 + c * 0.5) + c(0.5 + c)) = 0 ((0.25 + 0.5c) + c(0.5 + c)) = 0 (0.25 + 0.5c + (0.5 * c + c * c)) = 0 (0.25 + 0.5c + (0.5c + c2)) = 0 Combine like terms: 0.5c + 0.5c = 1c (0.25 + 1c + c2) = 0 Solving 0.25 + 1c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 1c + -0.25 + c2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 1c + c2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 1c + c2 = 0 + -0.25 1c + c2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 1c + c2 = -0.25 The c term is 1c. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. c + 0.25 + c2 = -0.25 + 0.25 Reorder the terms: 0.25 + c + c2 = -0.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.25 + c + c2 = 0.00 Factor a perfect square on the left side: (c + 0.5)(c + 0.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (c + 0.5) equal to 0.00 and 0.00.Subproblem 1
c + 0.5 = 0.00 Simplifying c + 0.5 = 0.00 Reorder the terms: 0.5 + c = 0.00 Solving 0.5 + c = 0.00 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + c = 0.00 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = 0.00 + -0.5 c = 0.00 + -0.5 Combine like terms: 0.00 + -0.5 = -0.5 c = -0.5 Simplifying c = -0.5Subproblem 2
c + 0.5 = 0.00 Simplifying c + 0.5 = 0.00 Reorder the terms: 0.5 + c = 0.00 Solving 0.5 + c = 0.00 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + c = 0.00 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = 0.00 + -0.5 c = 0.00 + -0.5 Combine like terms: 0.00 + -0.5 = -0.5 c = -0.5 Simplifying c = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. c = {-0.5, -0.5}
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