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Simplifying 10(c + 2) * c = 7 Reorder the terms: 10(2 + c) * c = 7 Reorder the terms for easier multiplication: 10c(2 + c) = 7 (2 * 10c + c * 10c) = 7 (20c + 10c2) = 7 Solving 20c + 10c2 = 7 Solving for variable 'c'. Reorder the terms: -7 + 20c + 10c2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 20c + 10c2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.7 + 2c + c2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + 2c + 0.7 + c2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + 2c + c2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + 2c + c2 = 0 + 0.7 2c + c2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 2c + c2 = 0.7 The c term is 2c. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2c + 1 + c2 = 0.7 + 1 Reorder the terms: 1 + 2c + c2 = 0.7 + 1 Combine like terms: 0.7 + 1 = 1.7 1 + 2c + c2 = 1.7 Factor a perfect square on the left side: (c + 1)(c + 1) = 1.7 Calculate the square root of the right side: 1.303840481 Break this problem into two subproblems by setting (c + 1) equal to 1.303840481 and -1.303840481.Subproblem 1
c + 1 = 1.303840481 Simplifying c + 1 = 1.303840481 Reorder the terms: 1 + c = 1.303840481 Solving 1 + c = 1.303840481 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + c = 1.303840481 + -1 Combine like terms: 1 + -1 = 0 0 + c = 1.303840481 + -1 c = 1.303840481 + -1 Combine like terms: 1.303840481 + -1 = 0.303840481 c = 0.303840481 Simplifying c = 0.303840481Subproblem 2
c + 1 = -1.303840481 Simplifying c + 1 = -1.303840481 Reorder the terms: 1 + c = -1.303840481 Solving 1 + c = -1.303840481 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + c = -1.303840481 + -1 Combine like terms: 1 + -1 = 0 0 + c = -1.303840481 + -1 c = -1.303840481 + -1 Combine like terms: -1.303840481 + -1 = -2.303840481 c = -2.303840481 Simplifying c = -2.303840481Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.303840481, -2.303840481}
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