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Simplifying 5b2 + -4b + -11 = 2b + -2 Reorder the terms: -11 + -4b + 5b2 = 2b + -2 Reorder the terms: -11 + -4b + 5b2 = -2 + 2b Solving -11 + -4b + 5b2 = -2 + 2b Solving for variable 'b'. Reorder the terms: -11 + 2 + -4b + -2b + 5b2 = -2 + 2b + 2 + -2b Combine like terms: -11 + 2 = -9 -9 + -4b + -2b + 5b2 = -2 + 2b + 2 + -2b Combine like terms: -4b + -2b = -6b -9 + -6b + 5b2 = -2 + 2b + 2 + -2b Reorder the terms: -9 + -6b + 5b2 = -2 + 2 + 2b + -2b Combine like terms: -2 + 2 = 0 -9 + -6b + 5b2 = 0 + 2b + -2b -9 + -6b + 5b2 = 2b + -2b Combine like terms: 2b + -2b = 0 -9 + -6b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + -1.2b + b2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -1.2b + 1.8 + b2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -1.2b + b2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -1.2b + b2 = 0 + 1.8 -1.2b + b2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -1.2b + b2 = 1.8 The b term is -1.2b. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2b + 0.36 + b2 = 1.8 + 0.36 Reorder the terms: 0.36 + -1.2b + b2 = 1.8 + 0.36 Combine like terms: 1.8 + 0.36 = 2.16 0.36 + -1.2b + b2 = 2.16 Factor a perfect square on the left side: (b + -0.6)(b + -0.6) = 2.16 Calculate the square root of the right side: 1.469693846 Break this problem into two subproblems by setting (b + -0.6) equal to 1.469693846 and -1.469693846.Subproblem 1
b + -0.6 = 1.469693846 Simplifying b + -0.6 = 1.469693846 Reorder the terms: -0.6 + b = 1.469693846 Solving -0.6 + b = 1.469693846 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + b = 1.469693846 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + b = 1.469693846 + 0.6 b = 1.469693846 + 0.6 Combine like terms: 1.469693846 + 0.6 = 2.069693846 b = 2.069693846 Simplifying b = 2.069693846Subproblem 2
b + -0.6 = -1.469693846 Simplifying b + -0.6 = -1.469693846 Reorder the terms: -0.6 + b = -1.469693846 Solving -0.6 + b = -1.469693846 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + b = -1.469693846 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + b = -1.469693846 + 0.6 b = -1.469693846 + 0.6 Combine like terms: -1.469693846 + 0.6 = -0.869693846 b = -0.869693846 Simplifying b = -0.869693846Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.069693846, -0.869693846}
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