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Simplifying 9b + 21b2 + -3 = 0 Reorder the terms: -3 + 9b + 21b2 = 0 Solving -3 + 9b + 21b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 3b + 7b2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 3b + 7b2)' equal to zero and attempt to solve: Simplifying -1 + 3b + 7b2 = 0 Solving -1 + 3b + 7b2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + 0.4285714286b + b2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.4285714286b + 0.1428571429 + b2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + 0.4285714286b + b2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + 0.4285714286b + b2 = 0 + 0.1428571429 0.4285714286b + b2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 0.4285714286b + b2 = 0.1428571429 The b term is 0.4285714286b. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286b + 0.04591836735 + b2 = 0.1428571429 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286b + b2 = 0.1428571429 + 0.04591836735 Combine like terms: 0.1428571429 + 0.04591836735 = 0.18877551025 0.04591836735 + 0.4285714286b + b2 = 0.18877551025 Factor a perfect square on the left side: (b + 0.2142857143)(b + 0.2142857143) = 0.18877551025 Calculate the square root of the right side: 0.434483038 Break this problem into two subproblems by setting (b + 0.2142857143) equal to 0.434483038 and -0.434483038.Subproblem 1
b + 0.2142857143 = 0.434483038 Simplifying b + 0.2142857143 = 0.434483038 Reorder the terms: 0.2142857143 + b = 0.434483038 Solving 0.2142857143 + b = 0.434483038 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + b = 0.434483038 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + b = 0.434483038 + -0.2142857143 b = 0.434483038 + -0.2142857143 Combine like terms: 0.434483038 + -0.2142857143 = 0.2201973237 b = 0.2201973237 Simplifying b = 0.2201973237Subproblem 2
b + 0.2142857143 = -0.434483038 Simplifying b + 0.2142857143 = -0.434483038 Reorder the terms: 0.2142857143 + b = -0.434483038 Solving 0.2142857143 + b = -0.434483038 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + b = -0.434483038 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + b = -0.434483038 + -0.2142857143 b = -0.434483038 + -0.2142857143 Combine like terms: -0.434483038 + -0.2142857143 = -0.6487687523 b = -0.6487687523 Simplifying b = -0.6487687523Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.2201973237, -0.6487687523}Solution
b = {0.2201973237, -0.6487687523}
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