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Simplifying b2 + -12b + -50 = 0 Reorder the terms: -50 + -12b + b2 = 0 Solving -50 + -12b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -12b + 50 + b2 = 0 + 50 Reorder the terms: -50 + 50 + -12b + b2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -12b + b2 = 0 + 50 -12b + b2 = 0 + 50 Combine like terms: 0 + 50 = 50 -12b + b2 = 50 The b term is -12b. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12b + 36 + b2 = 50 + 36 Reorder the terms: 36 + -12b + b2 = 50 + 36 Combine like terms: 50 + 36 = 86 36 + -12b + b2 = 86 Factor a perfect square on the left side: (b + -6)(b + -6) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (b + -6) equal to 9.273618495 and -9.273618495.Subproblem 1
b + -6 = 9.273618495 Simplifying b + -6 = 9.273618495 Reorder the terms: -6 + b = 9.273618495 Solving -6 + b = 9.273618495 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + b = 9.273618495 + 6 Combine like terms: -6 + 6 = 0 0 + b = 9.273618495 + 6 b = 9.273618495 + 6 Combine like terms: 9.273618495 + 6 = 15.273618495 b = 15.273618495 Simplifying b = 15.273618495Subproblem 2
b + -6 = -9.273618495 Simplifying b + -6 = -9.273618495 Reorder the terms: -6 + b = -9.273618495 Solving -6 + b = -9.273618495 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + b = -9.273618495 + 6 Combine like terms: -6 + 6 = 0 0 + b = -9.273618495 + 6 b = -9.273618495 + 6 Combine like terms: -9.273618495 + 6 = -3.273618495 b = -3.273618495 Simplifying b = -3.273618495Solution
The solution to the problem is based on the solutions from the subproblems. b = {15.273618495, -3.273618495}
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