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Simplifying 70b2 + -3b + -25 = 0 Reorder the terms: -25 + -3b + 70b2 = 0 Solving -25 + -3b + 70b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 70 the coefficient of the squared term: Divide each side by '70'. -0.3571428571 + -0.04285714286b + b2 = 0 Move the constant term to the right: Add '0.3571428571' to each side of the equation. -0.3571428571 + -0.04285714286b + 0.3571428571 + b2 = 0 + 0.3571428571 Reorder the terms: -0.3571428571 + 0.3571428571 + -0.04285714286b + b2 = 0 + 0.3571428571 Combine like terms: -0.3571428571 + 0.3571428571 = 0.0000000000 0.0000000000 + -0.04285714286b + b2 = 0 + 0.3571428571 -0.04285714286b + b2 = 0 + 0.3571428571 Combine like terms: 0 + 0.3571428571 = 0.3571428571 -0.04285714286b + b2 = 0.3571428571 The b term is -0.04285714286b. Take half its coefficient (-0.02142857143). Square it (0.0004591836735) and add it to both sides. Add '0.0004591836735' to each side of the equation. -0.04285714286b + 0.0004591836735 + b2 = 0.3571428571 + 0.0004591836735 Reorder the terms: 0.0004591836735 + -0.04285714286b + b2 = 0.3571428571 + 0.0004591836735 Combine like terms: 0.3571428571 + 0.0004591836735 = 0.3576020407735 0.0004591836735 + -0.04285714286b + b2 = 0.3576020407735 Factor a perfect square on the left side: (b + -0.02142857143)(b + -0.02142857143) = 0.3576020407735 Calculate the square root of the right side: 0.597998362 Break this problem into two subproblems by setting (b + -0.02142857143) equal to 0.597998362 and -0.597998362.Subproblem 1
b + -0.02142857143 = 0.597998362 Simplifying b + -0.02142857143 = 0.597998362 Reorder the terms: -0.02142857143 + b = 0.597998362 Solving -0.02142857143 + b = 0.597998362 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.02142857143' to each side of the equation. -0.02142857143 + 0.02142857143 + b = 0.597998362 + 0.02142857143 Combine like terms: -0.02142857143 + 0.02142857143 = 0.00000000000 0.00000000000 + b = 0.597998362 + 0.02142857143 b = 0.597998362 + 0.02142857143 Combine like terms: 0.597998362 + 0.02142857143 = 0.61942693343 b = 0.61942693343 Simplifying b = 0.61942693343Subproblem 2
b + -0.02142857143 = -0.597998362 Simplifying b + -0.02142857143 = -0.597998362 Reorder the terms: -0.02142857143 + b = -0.597998362 Solving -0.02142857143 + b = -0.597998362 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.02142857143' to each side of the equation. -0.02142857143 + 0.02142857143 + b = -0.597998362 + 0.02142857143 Combine like terms: -0.02142857143 + 0.02142857143 = 0.00000000000 0.00000000000 + b = -0.597998362 + 0.02142857143 b = -0.597998362 + 0.02142857143 Combine like terms: -0.597998362 + 0.02142857143 = -0.57656979057 b = -0.57656979057 Simplifying b = -0.57656979057Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.61942693343, -0.57656979057}
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