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Simplifying 11b2 + -10 = -9b Reorder the terms: -10 + 11b2 = -9b Solving -10 + 11b2 = -9b Solving for variable 'b'. Reorder the terms: -10 + 9b + 11b2 = -9b + 9b Combine like terms: -9b + 9b = 0 -10 + 9b + 11b2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.9090909091 + 0.8181818182b + b2 = 0 Move the constant term to the right: Add '0.9090909091' to each side of the equation. -0.9090909091 + 0.8181818182b + 0.9090909091 + b2 = 0 + 0.9090909091 Reorder the terms: -0.9090909091 + 0.9090909091 + 0.8181818182b + b2 = 0 + 0.9090909091 Combine like terms: -0.9090909091 + 0.9090909091 = 0.0000000000 0.0000000000 + 0.8181818182b + b2 = 0 + 0.9090909091 0.8181818182b + b2 = 0 + 0.9090909091 Combine like terms: 0 + 0.9090909091 = 0.9090909091 0.8181818182b + b2 = 0.9090909091 The b term is 0.8181818182b. Take half its coefficient (0.4090909091). Square it (0.1673553719) and add it to both sides. Add '0.1673553719' to each side of the equation. 0.8181818182b + 0.1673553719 + b2 = 0.9090909091 + 0.1673553719 Reorder the terms: 0.1673553719 + 0.8181818182b + b2 = 0.9090909091 + 0.1673553719 Combine like terms: 0.9090909091 + 0.1673553719 = 1.076446281 0.1673553719 + 0.8181818182b + b2 = 1.076446281 Factor a perfect square on the left side: (b + 0.4090909091)(b + 0.4090909091) = 1.076446281 Calculate the square root of the right side: 1.037519292 Break this problem into two subproblems by setting (b + 0.4090909091) equal to 1.037519292 and -1.037519292.Subproblem 1
b + 0.4090909091 = 1.037519292 Simplifying b + 0.4090909091 = 1.037519292 Reorder the terms: 0.4090909091 + b = 1.037519292 Solving 0.4090909091 + b = 1.037519292 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.4090909091' to each side of the equation. 0.4090909091 + -0.4090909091 + b = 1.037519292 + -0.4090909091 Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000 0.0000000000 + b = 1.037519292 + -0.4090909091 b = 1.037519292 + -0.4090909091 Combine like terms: 1.037519292 + -0.4090909091 = 0.6284283829 b = 0.6284283829 Simplifying b = 0.6284283829Subproblem 2
b + 0.4090909091 = -1.037519292 Simplifying b + 0.4090909091 = -1.037519292 Reorder the terms: 0.4090909091 + b = -1.037519292 Solving 0.4090909091 + b = -1.037519292 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.4090909091' to each side of the equation. 0.4090909091 + -0.4090909091 + b = -1.037519292 + -0.4090909091 Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000 0.0000000000 + b = -1.037519292 + -0.4090909091 b = -1.037519292 + -0.4090909091 Combine like terms: -1.037519292 + -0.4090909091 = -1.4466102011 b = -1.4466102011 Simplifying b = -1.4466102011Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.6284283829, -1.4466102011}
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