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Simplifying 2c2 + 14c = 10 Reorder the terms: 14c + 2c2 = 10 Solving 14c + 2c2 = 10 Solving for variable 'c'. Reorder the terms: -10 + 14c + 2c2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 14c + 2c2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 7c + c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 7c + c2)' equal to zero and attempt to solve: Simplifying -5 + 7c + c2 = 0 Solving -5 + 7c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 7c + 5 + c2 = 0 + 5 Reorder the terms: -5 + 5 + 7c + c2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 7c + c2 = 0 + 5 7c + c2 = 0 + 5 Combine like terms: 0 + 5 = 5 7c + c2 = 5 The c term is 7c. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7c + 12.25 + c2 = 5 + 12.25 Reorder the terms: 12.25 + 7c + c2 = 5 + 12.25 Combine like terms: 5 + 12.25 = 17.25 12.25 + 7c + c2 = 17.25 Factor a perfect square on the left side: (c + 3.5)(c + 3.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (c + 3.5) equal to 4.153311931 and -4.153311931.Subproblem 1
c + 3.5 = 4.153311931 Simplifying c + 3.5 = 4.153311931 Reorder the terms: 3.5 + c = 4.153311931 Solving 3.5 + c = 4.153311931 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + c = 4.153311931 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + c = 4.153311931 + -3.5 c = 4.153311931 + -3.5 Combine like terms: 4.153311931 + -3.5 = 0.653311931 c = 0.653311931 Simplifying c = 0.653311931Subproblem 2
c + 3.5 = -4.153311931 Simplifying c + 3.5 = -4.153311931 Reorder the terms: 3.5 + c = -4.153311931 Solving 3.5 + c = -4.153311931 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + c = -4.153311931 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + c = -4.153311931 + -3.5 c = -4.153311931 + -3.5 Combine like terms: -4.153311931 + -3.5 = -7.653311931 c = -7.653311931 Simplifying c = -7.653311931Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.653311931, -7.653311931}Solution
c = {0.653311931, -7.653311931}
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