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Simplifying c2 + -8c + -36 = 0 Reorder the terms: -36 + -8c + c2 = 0 Solving -36 + -8c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -8c + 36 + c2 = 0 + 36 Reorder the terms: -36 + 36 + -8c + c2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -8c + c2 = 0 + 36 -8c + c2 = 0 + 36 Combine like terms: 0 + 36 = 36 -8c + c2 = 36 The c term is -8c. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8c + 16 + c2 = 36 + 16 Reorder the terms: 16 + -8c + c2 = 36 + 16 Combine like terms: 36 + 16 = 52 16 + -8c + c2 = 52 Factor a perfect square on the left side: (c + -4)(c + -4) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (c + -4) equal to 7.211102551 and -7.211102551.Subproblem 1
c + -4 = 7.211102551 Simplifying c + -4 = 7.211102551 Reorder the terms: -4 + c = 7.211102551 Solving -4 + c = 7.211102551 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + c = 7.211102551 + 4 Combine like terms: -4 + 4 = 0 0 + c = 7.211102551 + 4 c = 7.211102551 + 4 Combine like terms: 7.211102551 + 4 = 11.211102551 c = 11.211102551 Simplifying c = 11.211102551Subproblem 2
c + -4 = -7.211102551 Simplifying c + -4 = -7.211102551 Reorder the terms: -4 + c = -7.211102551 Solving -4 + c = -7.211102551 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + c = -7.211102551 + 4 Combine like terms: -4 + 4 = 0 0 + c = -7.211102551 + 4 c = -7.211102551 + 4 Combine like terms: -7.211102551 + 4 = -3.211102551 c = -3.211102551 Simplifying c = -3.211102551Solution
The solution to the problem is based on the solutions from the subproblems. c = {11.211102551, -3.211102551}
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