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Simplifying c(c + 1) = 63 Reorder the terms: c(1 + c) = 63 (1 * c + c * c) = 63 (1c + c2) = 63 Solving 1c + c2 = 63 Solving for variable 'c'. Reorder the terms: -63 + 1c + c2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + 1c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + 1c + 63 + c2 = 0 + 63 Reorder the terms: -63 + 63 + 1c + c2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 1c + c2 = 0 + 63 1c + c2 = 0 + 63 Combine like terms: 0 + 63 = 63 1c + c2 = 63 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 = 63 + 0.25 Reorder the terms: 0.25 + c + c2 = 63 + 0.25 Combine like terms: 63 + 0.25 = 63.25 0.25 + c + c2 = 63.25 Factor a perfect square on the left side: (c + 0.5)(c + 0.5) = 63.25 Calculate the square root of the right side: 7.95298686 Break this problem into two subproblems by setting (c + 0.5) equal to 7.95298686 and -7.95298686.Subproblem 1
c + 0.5 = 7.95298686 Simplifying c + 0.5 = 7.95298686 Reorder the terms: 0.5 + c = 7.95298686 Solving 0.5 + c = 7.95298686 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 = 7.95298686 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = 7.95298686 + -0.5 c = 7.95298686 + -0.5 Combine like terms: 7.95298686 + -0.5 = 7.45298686 c = 7.45298686 Simplifying c = 7.45298686Subproblem 2
c + 0.5 = -7.95298686 Simplifying c + 0.5 = -7.95298686 Reorder the terms: 0.5 + c = -7.95298686 Solving 0.5 + c = -7.95298686 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 = -7.95298686 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + c = -7.95298686 + -0.5 c = -7.95298686 + -0.5 Combine like terms: -7.95298686 + -0.5 = -8.45298686 c = -8.45298686 Simplifying c = -8.45298686Solution
The solution to the problem is based on the solutions from the subproblems. c = {7.45298686, -8.45298686}
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