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Simplifying c2 + -7c = -3 Reorder the terms: -7c + c2 = -3 Solving -7c + c2 = -3 Solving for variable 'c'. Reorder the terms: 3 + -7c + c2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + -7c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -7c + -3 + c2 = 0 + -3 Reorder the terms: 3 + -3 + -7c + c2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7c + c2 = 0 + -3 -7c + c2 = 0 + -3 Combine like terms: 0 + -3 = -3 -7c + c2 = -3 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 = -3 + 12.25 Reorder the terms: 12.25 + -7c + c2 = -3 + 12.25 Combine like terms: -3 + 12.25 = 9.25 12.25 + -7c + c2 = 9.25 Factor a perfect square on the left side: (c + -3.5)(c + -3.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (c + -3.5) equal to 3.041381265 and -3.041381265.Subproblem 1
c + -3.5 = 3.041381265 Simplifying c + -3.5 = 3.041381265 Reorder the terms: -3.5 + c = 3.041381265 Solving -3.5 + c = 3.041381265 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 = 3.041381265 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + c = 3.041381265 + 3.5 c = 3.041381265 + 3.5 Combine like terms: 3.041381265 + 3.5 = 6.541381265 c = 6.541381265 Simplifying c = 6.541381265Subproblem 2
c + -3.5 = -3.041381265 Simplifying c + -3.5 = -3.041381265 Reorder the terms: -3.5 + c = -3.041381265 Solving -3.5 + c = -3.041381265 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 = -3.041381265 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + c = -3.041381265 + 3.5 c = -3.041381265 + 3.5 Combine like terms: -3.041381265 + 3.5 = 0.458618735 c = 0.458618735 Simplifying c = 0.458618735Solution
The solution to the problem is based on the solutions from the subproblems. c = {6.541381265, 0.458618735}
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