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Simplifying 9b2 + -15b + 4 = 8 Reorder the terms: 4 + -15b + 9b2 = 8 Solving 4 + -15b + 9b2 = 8 Solving for variable 'b'. Reorder the terms: 4 + -8 + -15b + 9b2 = 8 + -8 Combine like terms: 4 + -8 = -4 -4 + -15b + 9b2 = 8 + -8 Combine like terms: 8 + -8 = 0 -4 + -15b + 9b2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + -1.666666667b + b2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -1.666666667b + 0.4444444444 + b2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -1.666666667b + b2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -1.666666667b + b2 = 0 + 0.4444444444 -1.666666667b + b2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -1.666666667b + b2 = 0.4444444444 The b term is -1.666666667b. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667b + 0.6944444447 + b2 = 0.4444444444 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667b + b2 = 0.4444444444 + 0.6944444447 Combine like terms: 0.4444444444 + 0.6944444447 = 1.1388888891 0.6944444447 + -1.666666667b + b2 = 1.1388888891 Factor a perfect square on the left side: (b + -0.8333333335)(b + -0.8333333335) = 1.1388888891 Calculate the square root of the right side: 1.067187373 Break this problem into two subproblems by setting (b + -0.8333333335) equal to 1.067187373 and -1.067187373.Subproblem 1
b + -0.8333333335 = 1.067187373 Simplifying b + -0.8333333335 = 1.067187373 Reorder the terms: -0.8333333335 + b = 1.067187373 Solving -0.8333333335 + b = 1.067187373 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + b = 1.067187373 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + b = 1.067187373 + 0.8333333335 b = 1.067187373 + 0.8333333335 Combine like terms: 1.067187373 + 0.8333333335 = 1.9005207065 b = 1.9005207065 Simplifying b = 1.9005207065Subproblem 2
b + -0.8333333335 = -1.067187373 Simplifying b + -0.8333333335 = -1.067187373 Reorder the terms: -0.8333333335 + b = -1.067187373 Solving -0.8333333335 + b = -1.067187373 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + b = -1.067187373 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + b = -1.067187373 + 0.8333333335 b = -1.067187373 + 0.8333333335 Combine like terms: -1.067187373 + 0.8333333335 = -0.2338540395 b = -0.2338540395 Simplifying b = -0.2338540395Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.9005207065, -0.2338540395}
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