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Simplifying 3c2 + c + -10 = c2 + -5 Reorder the terms: -10 + c + 3c2 = c2 + -5 Reorder the terms: -10 + c + 3c2 = -5 + c2 Solving -10 + c + 3c2 = -5 + c2 Solving for variable 'c'. Reorder the terms: -10 + 5 + c + 3c2 + -1c2 = -5 + c2 + 5 + -1c2 Combine like terms: -10 + 5 = -5 -5 + c + 3c2 + -1c2 = -5 + c2 + 5 + -1c2 Combine like terms: 3c2 + -1c2 = 2c2 -5 + c + 2c2 = -5 + c2 + 5 + -1c2 Reorder the terms: -5 + c + 2c2 = -5 + 5 + c2 + -1c2 Combine like terms: -5 + 5 = 0 -5 + c + 2c2 = 0 + c2 + -1c2 -5 + c + 2c2 = c2 + -1c2 Combine like terms: c2 + -1c2 = 0 -5 + c + 2c2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 0.5c + c2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 0.5c + 2.5 + c2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 0.5c + c2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 0.5c + c2 = 0 + 2.5 0.5c + c2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 0.5c + c2 = 2.5 The c term is c. 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. 0.5c + 0.25 + c2 = 2.5 + 0.25 Reorder the terms: 0.25 + 0.5c + c2 = 2.5 + 0.25 Combine like terms: 2.5 + 0.25 = 2.75 0.25 + 0.5c + c2 = 2.75 Factor a perfect square on the left side: (c + 0.5)(c + 0.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (c + 0.5) equal to 1.658312395 and -1.658312395.Subproblem 1
c + 0.5 = 1.658312395 Simplifying c + 0.5 = 1.658312395 Reorder the terms: 0.5 + c = 1.658312395 Solving 0.5 + c = 1.658312395 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 = 1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = 1.658312395 + -0.5 c = 1.658312395 + -0.5 Combine like terms: 1.658312395 + -0.5 = 1.158312395 c = 1.158312395 Simplifying c = 1.158312395Subproblem 2
c + 0.5 = -1.658312395 Simplifying c + 0.5 = -1.658312395 Reorder the terms: 0.5 + c = -1.658312395 Solving 0.5 + c = -1.658312395 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 = -1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = -1.658312395 + -0.5 c = -1.658312395 + -0.5 Combine like terms: -1.658312395 + -0.5 = -2.158312395 c = -2.158312395 Simplifying c = -2.158312395Solution
The solution to the problem is based on the solutions from the subproblems. c = {1.158312395, -2.158312395}
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