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Simplifying c2 + -10c + 6 = 0 Reorder the terms: 6 + -10c + c2 = 0 Solving 6 + -10c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -10c + -6 + c2 = 0 + -6 Reorder the terms: 6 + -6 + -10c + c2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -10c + c2 = 0 + -6 -10c + c2 = 0 + -6 Combine like terms: 0 + -6 = -6 -10c + c2 = -6 The c term is -10c. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10c + 25 + c2 = -6 + 25 Reorder the terms: 25 + -10c + c2 = -6 + 25 Combine like terms: -6 + 25 = 19 25 + -10c + c2 = 19 Factor a perfect square on the left side: (c + -5)(c + -5) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (c + -5) equal to 4.358898944 and -4.358898944.Subproblem 1
c + -5 = 4.358898944 Simplifying c + -5 = 4.358898944 Reorder the terms: -5 + c = 4.358898944 Solving -5 + c = 4.358898944 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + c = 4.358898944 + 5 Combine like terms: -5 + 5 = 0 0 + c = 4.358898944 + 5 c = 4.358898944 + 5 Combine like terms: 4.358898944 + 5 = 9.358898944 c = 9.358898944 Simplifying c = 9.358898944Subproblem 2
c + -5 = -4.358898944 Simplifying c + -5 = -4.358898944 Reorder the terms: -5 + c = -4.358898944 Solving -5 + c = -4.358898944 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + c = -4.358898944 + 5 Combine like terms: -5 + 5 = 0 0 + c = -4.358898944 + 5 c = -4.358898944 + 5 Combine like terms: -4.358898944 + 5 = 0.641101056 c = 0.641101056 Simplifying c = 0.641101056Solution
The solution to the problem is based on the solutions from the subproblems. c = {9.358898944, 0.641101056}
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