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Simplifying 10b4 + 3b2 + -11 = 0 Reorder the terms: -11 + 3b2 + 10b4 = 0 Solving -11 + 3b2 + 10b4 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.1 + 0.3b2 + b4 = 0 Move the constant term to the right: Add '1.1' to each side of the equation. -1.1 + 0.3b2 + 1.1 + b4 = 0 + 1.1 Reorder the terms: -1.1 + 1.1 + 0.3b2 + b4 = 0 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + 0.3b2 + b4 = 0 + 1.1 0.3b2 + b4 = 0 + 1.1 Combine like terms: 0 + 1.1 = 1.1 0.3b2 + b4 = 1.1 The b term is 0.3b2. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3b2 + 0.0225 + b4 = 1.1 + 0.0225 Reorder the terms: 0.0225 + 0.3b2 + b4 = 1.1 + 0.0225 Combine like terms: 1.1 + 0.0225 = 1.1225 0.0225 + 0.3b2 + b4 = 1.1225 Factor a perfect square on the left side: (b2 + 0.15)(b2 + 0.15) = 1.1225 Calculate the square root of the right side: 1.059481005 Break this problem into two subproblems by setting (b2 + 0.15) equal to 1.059481005 and -1.059481005.Subproblem 1
b2 + 0.15 = 1.059481005 Simplifying b2 + 0.15 = 1.059481005 Reorder the terms: 0.15 + b2 = 1.059481005 Solving 0.15 + b2 = 1.059481005 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + b2 = 1.059481005 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + b2 = 1.059481005 + -0.15 b2 = 1.059481005 + -0.15 Combine like terms: 1.059481005 + -0.15 = 0.909481005 b2 = 0.909481005 Simplifying b2 = 0.909481005 Take the square root of each side: b = {-0.953667135, 0.953667135}Subproblem 2
b2 + 0.15 = -1.059481005 Simplifying b2 + 0.15 = -1.059481005 Reorder the terms: 0.15 + b2 = -1.059481005 Solving 0.15 + b2 = -1.059481005 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + b2 = -1.059481005 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + b2 = -1.059481005 + -0.15 b2 = -1.059481005 + -0.15 Combine like terms: -1.059481005 + -0.15 = -1.209481005 b2 = -1.209481005 Simplifying b2 = -1.209481005 Reorder the terms: 1.209481005 + b2 = -1.209481005 + 1.209481005 Combine like terms: -1.209481005 + 1.209481005 = 0.000000000 1.209481005 + b2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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