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Simplifying 5b2 + -5b + -12 = 0 Reorder the terms: -12 + -5b + 5b2 = 0 Solving -12 + -5b + 5b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + -1b + b2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -1b + 2.4 + b2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -1b + b2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -1b + b2 = 0 + 2.4 -1b + b2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -1b + b2 = 2.4 The b term is -1b. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1b + 0.25 + b2 = 2.4 + 0.25 Reorder the terms: 0.25 + -1b + b2 = 2.4 + 0.25 Combine like terms: 2.4 + 0.25 = 2.65 0.25 + -1b + b2 = 2.65 Factor a perfect square on the left side: (b + -0.5)(b + -0.5) = 2.65 Calculate the square root of the right side: 1.62788206 Break this problem into two subproblems by setting (b + -0.5) equal to 1.62788206 and -1.62788206.Subproblem 1
b + -0.5 = 1.62788206 Simplifying b + -0.5 = 1.62788206 Reorder the terms: -0.5 + b = 1.62788206 Solving -0.5 + b = 1.62788206 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = 1.62788206 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = 1.62788206 + 0.5 b = 1.62788206 + 0.5 Combine like terms: 1.62788206 + 0.5 = 2.12788206 b = 2.12788206 Simplifying b = 2.12788206Subproblem 2
b + -0.5 = -1.62788206 Simplifying b + -0.5 = -1.62788206 Reorder the terms: -0.5 + b = -1.62788206 Solving -0.5 + b = -1.62788206 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + b = -1.62788206 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + b = -1.62788206 + 0.5 b = -1.62788206 + 0.5 Combine like terms: -1.62788206 + 0.5 = -1.12788206 b = -1.12788206 Simplifying b = -1.12788206Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.12788206, -1.12788206}
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