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Simplifying (21 + 10) * 21 = (c + 13) * c Combine like terms: 21 + 10 = 31 (31) * 21 = (c + 13) * c Multiply 31 * 21 651 = (c + 13) * c Reorder the terms: 651 = (13 + c) * c Reorder the terms for easier multiplication: 651 = c(13 + c) 651 = (13 * c + c * c) 651 = (13c + c2) Solving 651 = 13c + c2 Solving for variable 'c'. Reorder the terms: 651 + -13c + -1c2 = 13c + -13c + c2 + -1c2 Combine like terms: 13c + -13c = 0 651 + -13c + -1c2 = 0 + c2 + -1c2 651 + -13c + -1c2 = c2 + -1c2 Combine like terms: c2 + -1c2 = 0 651 + -13c + -1c2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -651 + 13c + c2 = 0 Move the constant term to the right: Add '651' to each side of the equation. -651 + 13c + 651 + c2 = 0 + 651 Reorder the terms: -651 + 651 + 13c + c2 = 0 + 651 Combine like terms: -651 + 651 = 0 0 + 13c + c2 = 0 + 651 13c + c2 = 0 + 651 Combine like terms: 0 + 651 = 651 13c + c2 = 651 The c term is 13c. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13c + 42.25 + c2 = 651 + 42.25 Reorder the terms: 42.25 + 13c + c2 = 651 + 42.25 Combine like terms: 651 + 42.25 = 693.25 42.25 + 13c + c2 = 693.25 Factor a perfect square on the left side: (c + 6.5)(c + 6.5) = 693.25 Calculate the square root of the right side: 26.329641091 Break this problem into two subproblems by setting (c + 6.5) equal to 26.329641091 and -26.329641091.Subproblem 1
c + 6.5 = 26.329641091 Simplifying c + 6.5 = 26.329641091 Reorder the terms: 6.5 + c = 26.329641091 Solving 6.5 + c = 26.329641091 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + c = 26.329641091 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + c = 26.329641091 + -6.5 c = 26.329641091 + -6.5 Combine like terms: 26.329641091 + -6.5 = 19.829641091 c = 19.829641091 Simplifying c = 19.829641091Subproblem 2
c + 6.5 = -26.329641091 Simplifying c + 6.5 = -26.329641091 Reorder the terms: 6.5 + c = -26.329641091 Solving 6.5 + c = -26.329641091 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + c = -26.329641091 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + c = -26.329641091 + -6.5 c = -26.329641091 + -6.5 Combine like terms: -26.329641091 + -6.5 = -32.829641091 c = -32.829641091 Simplifying c = -32.829641091Solution
The solution to the problem is based on the solutions from the subproblems. c = {19.829641091, -32.829641091}
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