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Simplifying 6b2 + 25b = 11 Reorder the terms: 25b + 6b2 = 11 Solving 25b + 6b2 = 11 Solving for variable 'b'. Reorder the terms: -11 + 25b + 6b2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 25b + 6b2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.833333333 + 4.166666667b + b2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + 4.166666667b + 1.833333333 + b2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + 4.166666667b + b2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + 4.166666667b + b2 = 0 + 1.833333333 4.166666667b + b2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 4.166666667b + b2 = 1.833333333 The b term is 4.166666667b. Take half its coefficient (2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. 4.166666667b + 4.340277781 + b2 = 1.833333333 + 4.340277781 Reorder the terms: 4.340277781 + 4.166666667b + b2 = 1.833333333 + 4.340277781 Combine like terms: 1.833333333 + 4.340277781 = 6.173611114 4.340277781 + 4.166666667b + b2 = 6.173611114 Factor a perfect square on the left side: (b + 2.083333334)(b + 2.083333334) = 6.173611114 Calculate the square root of the right side: 2.484675253 Break this problem into two subproblems by setting (b + 2.083333334) equal to 2.484675253 and -2.484675253.Subproblem 1
b + 2.083333334 = 2.484675253 Simplifying b + 2.083333334 = 2.484675253 Reorder the terms: 2.083333334 + b = 2.484675253 Solving 2.083333334 + b = 2.484675253 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + b = 2.484675253 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + b = 2.484675253 + -2.083333334 b = 2.484675253 + -2.083333334 Combine like terms: 2.484675253 + -2.083333334 = 0.401341919 b = 0.401341919 Simplifying b = 0.401341919Subproblem 2
b + 2.083333334 = -2.484675253 Simplifying b + 2.083333334 = -2.484675253 Reorder the terms: 2.083333334 + b = -2.484675253 Solving 2.083333334 + b = -2.484675253 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.083333334' to each side of the equation. 2.083333334 + -2.083333334 + b = -2.484675253 + -2.083333334 Combine like terms: 2.083333334 + -2.083333334 = 0.000000000 0.000000000 + b = -2.484675253 + -2.083333334 b = -2.484675253 + -2.083333334 Combine like terms: -2.484675253 + -2.083333334 = -4.568008587 b = -4.568008587 Simplifying b = -4.568008587Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.401341919, -4.568008587}
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