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Simplifying c2 + -10c + 12 = 0 Reorder the terms: 12 + -10c + c2 = 0 Solving 12 + -10c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -10c + -12 + c2 = 0 + -12 Reorder the terms: 12 + -12 + -10c + c2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -10c + c2 = 0 + -12 -10c + c2 = 0 + -12 Combine like terms: 0 + -12 = -12 -10c + c2 = -12 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 = -12 + 25 Reorder the terms: 25 + -10c + c2 = -12 + 25 Combine like terms: -12 + 25 = 13 25 + -10c + c2 = 13 Factor a perfect square on the left side: (c + -5)(c + -5) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (c + -5) equal to 3.605551275 and -3.605551275.Subproblem 1
c + -5 = 3.605551275 Simplifying c + -5 = 3.605551275 Reorder the terms: -5 + c = 3.605551275 Solving -5 + c = 3.605551275 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 = 3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + c = 3.605551275 + 5 c = 3.605551275 + 5 Combine like terms: 3.605551275 + 5 = 8.605551275 c = 8.605551275 Simplifying c = 8.605551275Subproblem 2
c + -5 = -3.605551275 Simplifying c + -5 = -3.605551275 Reorder the terms: -5 + c = -3.605551275 Solving -5 + c = -3.605551275 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 = -3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + c = -3.605551275 + 5 c = -3.605551275 + 5 Combine like terms: -3.605551275 + 5 = 1.394448725 c = 1.394448725 Simplifying c = 1.394448725Solution
The solution to the problem is based on the solutions from the subproblems. c = {8.605551275, 1.394448725}
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