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Simplifying -262 + 30c + c2 = 0 Solving -262 + 30c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '262' to each side of the equation. -262 + 30c + 262 + c2 = 0 + 262 Reorder the terms: -262 + 262 + 30c + c2 = 0 + 262 Combine like terms: -262 + 262 = 0 0 + 30c + c2 = 0 + 262 30c + c2 = 0 + 262 Combine like terms: 0 + 262 = 262 30c + c2 = 262 The c term is 30c. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30c + 225 + c2 = 262 + 225 Reorder the terms: 225 + 30c + c2 = 262 + 225 Combine like terms: 262 + 225 = 487 225 + 30c + c2 = 487 Factor a perfect square on the left side: (c + 15)(c + 15) = 487 Calculate the square root of the right side: 22.068076491 Break this problem into two subproblems by setting (c + 15) equal to 22.068076491 and -22.068076491.Subproblem 1
c + 15 = 22.068076491 Simplifying c + 15 = 22.068076491 Reorder the terms: 15 + c = 22.068076491 Solving 15 + c = 22.068076491 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + c = 22.068076491 + -15 Combine like terms: 15 + -15 = 0 0 + c = 22.068076491 + -15 c = 22.068076491 + -15 Combine like terms: 22.068076491 + -15 = 7.068076491 c = 7.068076491 Simplifying c = 7.068076491Subproblem 2
c + 15 = -22.068076491 Simplifying c + 15 = -22.068076491 Reorder the terms: 15 + c = -22.068076491 Solving 15 + c = -22.068076491 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + c = -22.068076491 + -15 Combine like terms: 15 + -15 = 0 0 + c = -22.068076491 + -15 c = -22.068076491 + -15 Combine like terms: -22.068076491 + -15 = -37.068076491 c = -37.068076491 Simplifying c = -37.068076491Solution
The solution to the problem is based on the solutions from the subproblems. c = {7.068076491, -37.068076491}
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