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Simplifying b2 + -15b + -12536 = 0 Reorder the terms: -12536 + -15b + b2 = 0 Solving -12536 + -15b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '12536' to each side of the equation. -12536 + -15b + 12536 + b2 = 0 + 12536 Reorder the terms: -12536 + 12536 + -15b + b2 = 0 + 12536 Combine like terms: -12536 + 12536 = 0 0 + -15b + b2 = 0 + 12536 -15b + b2 = 0 + 12536 Combine like terms: 0 + 12536 = 12536 -15b + b2 = 12536 The b term is -15b. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15b + 56.25 + b2 = 12536 + 56.25 Reorder the terms: 56.25 + -15b + b2 = 12536 + 56.25 Combine like terms: 12536 + 56.25 = 12592.25 56.25 + -15b + b2 = 12592.25 Factor a perfect square on the left side: (b + -7.5)(b + -7.5) = 12592.25 Calculate the square root of the right side: 112.21519505 Break this problem into two subproblems by setting (b + -7.5) equal to 112.21519505 and -112.21519505.Subproblem 1
b + -7.5 = 112.21519505 Simplifying b + -7.5 = 112.21519505 Reorder the terms: -7.5 + b = 112.21519505 Solving -7.5 + b = 112.21519505 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + b = 112.21519505 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + b = 112.21519505 + 7.5 b = 112.21519505 + 7.5 Combine like terms: 112.21519505 + 7.5 = 119.71519505 b = 119.71519505 Simplifying b = 119.71519505Subproblem 2
b + -7.5 = -112.21519505 Simplifying b + -7.5 = -112.21519505 Reorder the terms: -7.5 + b = -112.21519505 Solving -7.5 + b = -112.21519505 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + b = -112.21519505 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + b = -112.21519505 + 7.5 b = -112.21519505 + 7.5 Combine like terms: -112.21519505 + 7.5 = -104.71519505 b = -104.71519505 Simplifying b = -104.71519505Solution
The solution to the problem is based on the solutions from the subproblems. b = {119.71519505, -104.71519505}
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