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Simplifying 25 + -20c + c2 = 0 Solving 25 + -20c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -20c + -25 + c2 = 0 + -25 Reorder the terms: 25 + -25 + -20c + c2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -20c + c2 = 0 + -25 -20c + c2 = 0 + -25 Combine like terms: 0 + -25 = -25 -20c + c2 = -25 The c term is -20c. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20c + 100 + c2 = -25 + 100 Reorder the terms: 100 + -20c + c2 = -25 + 100 Combine like terms: -25 + 100 = 75 100 + -20c + c2 = 75 Factor a perfect square on the left side: (c + -10)(c + -10) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (c + -10) equal to 8.660254038 and -8.660254038.Subproblem 1
c + -10 = 8.660254038 Simplifying c + -10 = 8.660254038 Reorder the terms: -10 + c = 8.660254038 Solving -10 + c = 8.660254038 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + c = 8.660254038 + 10 Combine like terms: -10 + 10 = 0 0 + c = 8.660254038 + 10 c = 8.660254038 + 10 Combine like terms: 8.660254038 + 10 = 18.660254038 c = 18.660254038 Simplifying c = 18.660254038Subproblem 2
c + -10 = -8.660254038 Simplifying c + -10 = -8.660254038 Reorder the terms: -10 + c = -8.660254038 Solving -10 + c = -8.660254038 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + c = -8.660254038 + 10 Combine like terms: -10 + 10 = 0 0 + c = -8.660254038 + 10 c = -8.660254038 + 10 Combine like terms: -8.660254038 + 10 = 1.339745962 c = 1.339745962 Simplifying c = 1.339745962Solution
The solution to the problem is based on the solutions from the subproblems. c = {18.660254038, 1.339745962}
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