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Simplifying 7(c + 9) * c = 3 Reorder the terms: 7(9 + c) * c = 3 Reorder the terms for easier multiplication: 7c(9 + c) = 3 (9 * 7c + c * 7c) = 3 (63c + 7c2) = 3 Solving 63c + 7c2 = 3 Solving for variable 'c'. Reorder the terms: -3 + 63c + 7c2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 63c + 7c2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + 9c + c2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 9c + 0.4285714286 + c2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 9c + c2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 9c + c2 = 0 + 0.4285714286 9c + c2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 9c + c2 = 0.4285714286 The c term is 9c. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9c + 20.25 + c2 = 0.4285714286 + 20.25 Reorder the terms: 20.25 + 9c + c2 = 0.4285714286 + 20.25 Combine like terms: 0.4285714286 + 20.25 = 20.6785714286 20.25 + 9c + c2 = 20.6785714286 Factor a perfect square on the left side: (c + 4.5)(c + 4.5) = 20.6785714286 Calculate the square root of the right side: 4.547369726 Break this problem into two subproblems by setting (c + 4.5) equal to 4.547369726 and -4.547369726.Subproblem 1
c + 4.5 = 4.547369726 Simplifying c + 4.5 = 4.547369726 Reorder the terms: 4.5 + c = 4.547369726 Solving 4.5 + c = 4.547369726 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + c = 4.547369726 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + c = 4.547369726 + -4.5 c = 4.547369726 + -4.5 Combine like terms: 4.547369726 + -4.5 = 0.047369726 c = 0.047369726 Simplifying c = 0.047369726Subproblem 2
c + 4.5 = -4.547369726 Simplifying c + 4.5 = -4.547369726 Reorder the terms: 4.5 + c = -4.547369726 Solving 4.5 + c = -4.547369726 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + c = -4.547369726 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + c = -4.547369726 + -4.5 c = -4.547369726 + -4.5 Combine like terms: -4.547369726 + -4.5 = -9.047369726 c = -9.047369726 Simplifying c = -9.047369726Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.047369726, -9.047369726}
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