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Simplifying -3b2 + -11b = -15 Reorder the terms: -11b + -3b2 = -15 Solving -11b + -3b2 = -15 Solving for variable 'b'. Reorder the terms: 15 + -11b + -3b2 = -15 + 15 Combine like terms: -15 + 15 = 0 15 + -11b + -3b2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -5 + 3.666666667b + b2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 3.666666667b + 5 + b2 = 0 + 5 Reorder the terms: -5 + 5 + 3.666666667b + b2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3.666666667b + b2 = 0 + 5 3.666666667b + b2 = 0 + 5 Combine like terms: 0 + 5 = 5 3.666666667b + b2 = 5 The b term is 3.666666667b. Take half its coefficient (1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. 3.666666667b + 3.361111114 + b2 = 5 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667b + b2 = 5 + 3.361111114 Combine like terms: 5 + 3.361111114 = 8.361111114 3.361111114 + 3.666666667b + b2 = 8.361111114 Factor a perfect square on the left side: (b + 1.833333334)(b + 1.833333334) = 8.361111114 Calculate the square root of the right side: 2.891558596 Break this problem into two subproblems by setting (b + 1.833333334) equal to 2.891558596 and -2.891558596.Subproblem 1
b + 1.833333334 = 2.891558596 Simplifying b + 1.833333334 = 2.891558596 Reorder the terms: 1.833333334 + b = 2.891558596 Solving 1.833333334 + b = 2.891558596 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + b = 2.891558596 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + b = 2.891558596 + -1.833333334 b = 2.891558596 + -1.833333334 Combine like terms: 2.891558596 + -1.833333334 = 1.058225262 b = 1.058225262 Simplifying b = 1.058225262Subproblem 2
b + 1.833333334 = -2.891558596 Simplifying b + 1.833333334 = -2.891558596 Reorder the terms: 1.833333334 + b = -2.891558596 Solving 1.833333334 + b = -2.891558596 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + b = -2.891558596 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + b = -2.891558596 + -1.833333334 b = -2.891558596 + -1.833333334 Combine like terms: -2.891558596 + -1.833333334 = -4.72489193 b = -4.72489193 Simplifying b = -4.72489193Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.058225262, -4.72489193}
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