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Simplifying 7(c + 3) * c = 9 Reorder the terms: 7(3 + c) * c = 9 Reorder the terms for easier multiplication: 7c(3 + c) = 9 (3 * 7c + c * 7c) = 9 (21c + 7c2) = 9 Solving 21c + 7c2 = 9 Solving for variable 'c'. Reorder the terms: -9 + 21c + 7c2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 21c + 7c2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.285714286 + 3c + c2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + 3c + 1.285714286 + c2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + 3c + c2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + 3c + c2 = 0 + 1.285714286 3c + c2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 3c + c2 = 1.285714286 The c term is 3c. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3c + 2.25 + c2 = 1.285714286 + 2.25 Reorder the terms: 2.25 + 3c + c2 = 1.285714286 + 2.25 Combine like terms: 1.285714286 + 2.25 = 3.535714286 2.25 + 3c + c2 = 3.535714286 Factor a perfect square on the left side: (c + 1.5)(c + 1.5) = 3.535714286 Calculate the square root of the right side: 1.880349512 Break this problem into two subproblems by setting (c + 1.5) equal to 1.880349512 and -1.880349512.Subproblem 1
c + 1.5 = 1.880349512 Simplifying c + 1.5 = 1.880349512 Reorder the terms: 1.5 + c = 1.880349512 Solving 1.5 + c = 1.880349512 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + c = 1.880349512 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = 1.880349512 + -1.5 c = 1.880349512 + -1.5 Combine like terms: 1.880349512 + -1.5 = 0.380349512 c = 0.380349512 Simplifying c = 0.380349512Subproblem 2
c + 1.5 = -1.880349512 Simplifying c + 1.5 = -1.880349512 Reorder the terms: 1.5 + c = -1.880349512 Solving 1.5 + c = -1.880349512 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + c = -1.880349512 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + c = -1.880349512 + -1.5 c = -1.880349512 + -1.5 Combine like terms: -1.880349512 + -1.5 = -3.380349512 c = -3.380349512 Simplifying c = -3.380349512Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.380349512, -3.380349512}
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