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Simplifying 2b2 + -1b = 12 Reorder the terms: -1b + 2b2 = 12 Solving -1b + 2b2 = 12 Solving for variable 'b'. Reorder the terms: -12 + -1b + 2b2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -1b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + -0.5b + b2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -0.5b + 6 + b2 = 0 + 6 Reorder the terms: -6 + 6 + -0.5b + b2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -0.5b + b2 = 0 + 6 -0.5b + b2 = 0 + 6 Combine like terms: 0 + 6 = 6 -0.5b + b2 = 6 The b term is -0.5b. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5b + 0.0625 + b2 = 6 + 0.0625 Reorder the terms: 0.0625 + -0.5b + b2 = 6 + 0.0625 Combine like terms: 6 + 0.0625 = 6.0625 0.0625 + -0.5b + b2 = 6.0625 Factor a perfect square on the left side: (b + -0.25)(b + -0.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (b + -0.25) equal to 2.46221445 and -2.46221445.Subproblem 1
b + -0.25 = 2.46221445 Simplifying b + -0.25 = 2.46221445 Reorder the terms: -0.25 + b = 2.46221445 Solving -0.25 + b = 2.46221445 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + b = 2.46221445 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + b = 2.46221445 + 0.25 b = 2.46221445 + 0.25 Combine like terms: 2.46221445 + 0.25 = 2.71221445 b = 2.71221445 Simplifying b = 2.71221445Subproblem 2
b + -0.25 = -2.46221445 Simplifying b + -0.25 = -2.46221445 Reorder the terms: -0.25 + b = -2.46221445 Solving -0.25 + b = -2.46221445 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + b = -2.46221445 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + b = -2.46221445 + 0.25 b = -2.46221445 + 0.25 Combine like terms: -2.46221445 + 0.25 = -2.21221445 b = -2.21221445 Simplifying b = -2.21221445Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.71221445, -2.21221445}
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