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Simplifying 0 = c2 + -7c + -40 Reorder the terms: 0 = -40 + -7c + c2 Solving 0 = -40 + -7c + c2 Solving for variable 'c'. Combine like terms: 0 + 40 = 40 40 + 7c + -1c2 = -40 + -7c + c2 + 40 + 7c + -1c2 Reorder the terms: 40 + 7c + -1c2 = -40 + 40 + -7c + 7c + c2 + -1c2 Combine like terms: -40 + 40 = 0 40 + 7c + -1c2 = 0 + -7c + 7c + c2 + -1c2 40 + 7c + -1c2 = -7c + 7c + c2 + -1c2 Combine like terms: -7c + 7c = 0 40 + 7c + -1c2 = 0 + c2 + -1c2 40 + 7c + -1c2 = c2 + -1c2 Combine like terms: c2 + -1c2 = 0 40 + 7c + -1c2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + -7c + c2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -7c + 40 + c2 = 0 + 40 Reorder the terms: -40 + 40 + -7c + c2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -7c + c2 = 0 + 40 -7c + c2 = 0 + 40 Combine like terms: 0 + 40 = 40 -7c + c2 = 40 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 = 40 + 12.25 Reorder the terms: 12.25 + -7c + c2 = 40 + 12.25 Combine like terms: 40 + 12.25 = 52.25 12.25 + -7c + c2 = 52.25 Factor a perfect square on the left side: (c + -3.5)(c + -3.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (c + -3.5) equal to 7.228416147 and -7.228416147.Subproblem 1
c + -3.5 = 7.228416147 Simplifying c + -3.5 = 7.228416147 Reorder the terms: -3.5 + c = 7.228416147 Solving -3.5 + c = 7.228416147 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 = 7.228416147 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + c = 7.228416147 + 3.5 c = 7.228416147 + 3.5 Combine like terms: 7.228416147 + 3.5 = 10.728416147 c = 10.728416147 Simplifying c = 10.728416147Subproblem 2
c + -3.5 = -7.228416147 Simplifying c + -3.5 = -7.228416147 Reorder the terms: -3.5 + c = -7.228416147 Solving -3.5 + c = -7.228416147 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 = -7.228416147 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + c = -7.228416147 + 3.5 c = -7.228416147 + 3.5 Combine like terms: -7.228416147 + 3.5 = -3.728416147 c = -3.728416147 Simplifying c = -3.728416147Solution
The solution to the problem is based on the solutions from the subproblems. c = {10.728416147, -3.728416147}
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