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Simplifying 9b2 + -10b + 2 = 9 Reorder the terms: 2 + -10b + 9b2 = 9 Solving 2 + -10b + 9b2 = 9 Solving for variable 'b'. Reorder the terms: 2 + -9 + -10b + 9b2 = 9 + -9 Combine like terms: 2 + -9 = -7 -7 + -10b + 9b2 = 9 + -9 Combine like terms: 9 + -9 = 0 -7 + -10b + 9b2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.7777777778 + -1.111111111b + b2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + -1.111111111b + 0.7777777778 + b2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + -1.111111111b + b2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + -1.111111111b + b2 = 0 + 0.7777777778 -1.111111111b + b2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 -1.111111111b + b2 = 0.7777777778 The b term is -1.111111111b. Take half its coefficient (-0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. -1.111111111b + 0.3086419752 + b2 = 0.7777777778 + 0.3086419752 Reorder the terms: 0.3086419752 + -1.111111111b + b2 = 0.7777777778 + 0.3086419752 Combine like terms: 0.7777777778 + 0.3086419752 = 1.086419753 0.3086419752 + -1.111111111b + b2 = 1.086419753 Factor a perfect square on the left side: (b + -0.5555555555)(b + -0.5555555555) = 1.086419753 Calculate the square root of the right side: 1.042314613 Break this problem into two subproblems by setting (b + -0.5555555555) equal to 1.042314613 and -1.042314613.Subproblem 1
b + -0.5555555555 = 1.042314613 Simplifying b + -0.5555555555 = 1.042314613 Reorder the terms: -0.5555555555 + b = 1.042314613 Solving -0.5555555555 + b = 1.042314613 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + b = 1.042314613 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + b = 1.042314613 + 0.5555555555 b = 1.042314613 + 0.5555555555 Combine like terms: 1.042314613 + 0.5555555555 = 1.5978701685 b = 1.5978701685 Simplifying b = 1.5978701685Subproblem 2
b + -0.5555555555 = -1.042314613 Simplifying b + -0.5555555555 = -1.042314613 Reorder the terms: -0.5555555555 + b = -1.042314613 Solving -0.5555555555 + b = -1.042314613 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + b = -1.042314613 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + b = -1.042314613 + 0.5555555555 b = -1.042314613 + 0.5555555555 Combine like terms: -1.042314613 + 0.5555555555 = -0.4867590575 b = -0.4867590575 Simplifying b = -0.4867590575Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.5978701685, -0.4867590575}
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