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Simplifying 10b2 + -20b + -5 = 2 Reorder the terms: -5 + -20b + 10b2 = 2 Solving -5 + -20b + 10b2 = 2 Solving for variable 'b'. Reorder the terms: -5 + -2 + -20b + 10b2 = 2 + -2 Combine like terms: -5 + -2 = -7 -7 + -20b + 10b2 = 2 + -2 Combine like terms: 2 + -2 = 0 -7 + -20b + 10b2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.7 + -2b + b2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + -2b + 0.7 + b2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + -2b + b2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + -2b + b2 = 0 + 0.7 -2b + b2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 -2b + b2 = 0.7 The b term is -2b. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2b + 1 + b2 = 0.7 + 1 Reorder the terms: 1 + -2b + b2 = 0.7 + 1 Combine like terms: 0.7 + 1 = 1.7 1 + -2b + b2 = 1.7 Factor a perfect square on the left side: (b + -1)(b + -1) = 1.7 Calculate the square root of the right side: 1.303840481 Break this problem into two subproblems by setting (b + -1) equal to 1.303840481 and -1.303840481.Subproblem 1
b + -1 = 1.303840481 Simplifying b + -1 = 1.303840481 Reorder the terms: -1 + b = 1.303840481 Solving -1 + b = 1.303840481 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = 1.303840481 + 1 Combine like terms: -1 + 1 = 0 0 + b = 1.303840481 + 1 b = 1.303840481 + 1 Combine like terms: 1.303840481 + 1 = 2.303840481 b = 2.303840481 Simplifying b = 2.303840481Subproblem 2
b + -1 = -1.303840481 Simplifying b + -1 = -1.303840481 Reorder the terms: -1 + b = -1.303840481 Solving -1 + b = -1.303840481 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = -1.303840481 + 1 Combine like terms: -1 + 1 = 0 0 + b = -1.303840481 + 1 b = -1.303840481 + 1 Combine like terms: -1.303840481 + 1 = -0.303840481 b = -0.303840481 Simplifying b = -0.303840481Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.303840481, -0.303840481}
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