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Simplifying b2 + -3b + -70 = 70 Reorder the terms: -70 + -3b + b2 = 70 Solving -70 + -3b + b2 = 70 Solving for variable 'b'. Reorder the terms: -70 + -70 + -3b + b2 = 70 + -70 Combine like terms: -70 + -70 = -140 -140 + -3b + b2 = 70 + -70 Combine like terms: 70 + -70 = 0 -140 + -3b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + -3b + 140 + b2 = 0 + 140 Reorder the terms: -140 + 140 + -3b + b2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -3b + b2 = 0 + 140 -3b + b2 = 0 + 140 Combine like terms: 0 + 140 = 140 -3b + b2 = 140 The b term is -3b. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3b + 2.25 + b2 = 140 + 2.25 Reorder the terms: 2.25 + -3b + b2 = 140 + 2.25 Combine like terms: 140 + 2.25 = 142.25 2.25 + -3b + b2 = 142.25 Factor a perfect square on the left side: (b + -1.5)(b + -1.5) = 142.25 Calculate the square root of the right side: 11.926860442 Break this problem into two subproblems by setting (b + -1.5) equal to 11.926860442 and -11.926860442.Subproblem 1
b + -1.5 = 11.926860442 Simplifying b + -1.5 = 11.926860442 Reorder the terms: -1.5 + b = 11.926860442 Solving -1.5 + b = 11.926860442 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + b = 11.926860442 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = 11.926860442 + 1.5 b = 11.926860442 + 1.5 Combine like terms: 11.926860442 + 1.5 = 13.426860442 b = 13.426860442 Simplifying b = 13.426860442Subproblem 2
b + -1.5 = -11.926860442 Simplifying b + -1.5 = -11.926860442 Reorder the terms: -1.5 + b = -11.926860442 Solving -1.5 + b = -11.926860442 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + b = -11.926860442 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = -11.926860442 + 1.5 b = -11.926860442 + 1.5 Combine like terms: -11.926860442 + 1.5 = -10.426860442 b = -10.426860442 Simplifying b = -10.426860442Solution
The solution to the problem is based on the solutions from the subproblems. b = {13.426860442, -10.426860442}
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