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Simplifying 0 = 3b4 + 5.729577951b2 + -8.207015875 Reorder the terms: 0 = -8.207015875 + 5.729577951b2 + 3b4 Solving 0 = -8.207015875 + 5.729577951b2 + 3b4 Solving for variable 'b'. Combine like terms: 0 + 8.207015875 = 8.207015875 8.207015875 + -5.729577951b2 + -3b4 = -8.207015875 + 5.729577951b2 + 3b4 + 8.207015875 + -5.729577951b2 + -3b4 Reorder the terms: 8.207015875 + -5.729577951b2 + -3b4 = -8.207015875 + 8.207015875 + 5.729577951b2 + -5.729577951b2 + 3b4 + -3b4 Combine like terms: -8.207015875 + 8.207015875 = 0.000000000 8.207015875 + -5.729577951b2 + -3b4 = 0.000000000 + 5.729577951b2 + -5.729577951b2 + 3b4 + -3b4 8.207015875 + -5.729577951b2 + -3b4 = 5.729577951b2 + -5.729577951b2 + 3b4 + -3b4 Combine like terms: 5.729577951b2 + -5.729577951b2 = 0.000000000 8.207015875 + -5.729577951b2 + -3b4 = 0.000000000 + 3b4 + -3b4 8.207015875 + -5.729577951b2 + -3b4 = 3b4 + -3b4 Combine like terms: 3b4 + -3b4 = 0 8.207015875 + -5.729577951b2 + -3b4 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2.735671958 + 1.909859317b2 + b4 = 0 Move the constant term to the right: Add '2.735671958' to each side of the equation. -2.735671958 + 1.909859317b2 + 2.735671958 + b4 = 0 + 2.735671958 Reorder the terms: -2.735671958 + 2.735671958 + 1.909859317b2 + b4 = 0 + 2.735671958 Combine like terms: -2.735671958 + 2.735671958 = 0.000000000 0.000000000 + 1.909859317b2 + b4 = 0 + 2.735671958 1.909859317b2 + b4 = 0 + 2.735671958 Combine like terms: 0 + 2.735671958 = 2.735671958 1.909859317b2 + b4 = 2.735671958 The b term is 1.909859317b2. Take half its coefficient (0.9549296585). Square it (0.9118906527) and add it to both sides. Add '0.9118906527' to each side of the equation. 1.909859317b2 + 0.9118906527 + b4 = 2.735671958 + 0.9118906527 Reorder the terms: 0.9118906527 + 1.909859317b2 + b4 = 2.735671958 + 0.9118906527 Combine like terms: 2.735671958 + 0.9118906527 = 3.6475626107 0.9118906527 + 1.909859317b2 + b4 = 3.6475626107 Factor a perfect square on the left side: (b2 + 0.9549296585)(b2 + 0.9549296585) = 3.6475626107 Calculate the square root of the right side: 1.909859317 Break this problem into two subproblems by setting (b2 + 0.9549296585) equal to 1.909859317 and -1.909859317.Subproblem 1
b2 + 0.9549296585 = 1.909859317 Simplifying b2 + 0.9549296585 = 1.909859317 Reorder the terms: 0.9549296585 + b2 = 1.909859317 Solving 0.9549296585 + b2 = 1.909859317 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.9549296585' to each side of the equation. 0.9549296585 + -0.9549296585 + b2 = 1.909859317 + -0.9549296585 Combine like terms: 0.9549296585 + -0.9549296585 = 0.0000000000 0.0000000000 + b2 = 1.909859317 + -0.9549296585 b2 = 1.909859317 + -0.9549296585 Combine like terms: 1.909859317 + -0.9549296585 = 0.9549296585 b2 = 0.9549296585 Simplifying b2 = 0.9549296585 Take the square root of each side: b = {-0.977205024, 0.977205024}Subproblem 2
b2 + 0.9549296585 = -1.909859317 Simplifying b2 + 0.9549296585 = -1.909859317 Reorder the terms: 0.9549296585 + b2 = -1.909859317 Solving 0.9549296585 + b2 = -1.909859317 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.9549296585' to each side of the equation. 0.9549296585 + -0.9549296585 + b2 = -1.909859317 + -0.9549296585 Combine like terms: 0.9549296585 + -0.9549296585 = 0.0000000000 0.0000000000 + b2 = -1.909859317 + -0.9549296585 b2 = -1.909859317 + -0.9549296585 Combine like terms: -1.909859317 + -0.9549296585 = -2.8647889755 b2 = -2.8647889755 Simplifying b2 = -2.8647889755 Reorder the terms: 2.8647889755 + b2 = -2.8647889755 + 2.8647889755 Combine like terms: -2.8647889755 + 2.8647889755 = 0.0000000000 2.8647889755 + b2 = 0.0000000000 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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