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Simplifying 12b2 + -72b = 12 Reorder the terms: -72b + 12b2 = 12 Solving -72b + 12b2 = 12 Solving for variable 'b'. Reorder the terms: -12 + -72b + 12b2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -72b + 12b2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(-1 + -6b + b2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-1 + -6b + b2)' equal to zero and attempt to solve: Simplifying -1 + -6b + b2 = 0 Solving -1 + -6b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -6b + 1 + b2 = 0 + 1 Reorder the terms: -1 + 1 + -6b + b2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6b + b2 = 0 + 1 -6b + b2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6b + b2 = 1 The b term is -6b. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6b + 9 + b2 = 1 + 9 Reorder the terms: 9 + -6b + b2 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + -6b + b2 = 10 Factor a perfect square on the left side: (b + -3)(b + -3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (b + -3) equal to 3.16227766 and -3.16227766.Subproblem 1
b + -3 = 3.16227766 Simplifying b + -3 = 3.16227766 Reorder the terms: -3 + b = 3.16227766 Solving -3 + b = 3.16227766 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + b = 3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + b = 3.16227766 + 3 b = 3.16227766 + 3 Combine like terms: 3.16227766 + 3 = 6.16227766 b = 6.16227766 Simplifying b = 6.16227766Subproblem 2
b + -3 = -3.16227766 Simplifying b + -3 = -3.16227766 Reorder the terms: -3 + b = -3.16227766 Solving -3 + b = -3.16227766 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + b = -3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + b = -3.16227766 + 3 b = -3.16227766 + 3 Combine like terms: -3.16227766 + 3 = -0.16227766 b = -0.16227766 Simplifying b = -0.16227766Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.16227766, -0.16227766}Solution
b = {6.16227766, -0.16227766}
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