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Simplifying (b + -3) * b = 35 Reorder the terms: (-3 + b) * b = 35 Reorder the terms for easier multiplication: b(-3 + b) = 35 (-3 * b + b * b) = 35 (-3b + b2) = 35 Solving -3b + b2 = 35 Solving for variable 'b'. Reorder the terms: -35 + -3b + b2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -3b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -3b + 35 + b2 = 0 + 35 Reorder the terms: -35 + 35 + -3b + b2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -3b + b2 = 0 + 35 -3b + b2 = 0 + 35 Combine like terms: 0 + 35 = 35 -3b + b2 = 35 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 = 35 + 2.25 Reorder the terms: 2.25 + -3b + b2 = 35 + 2.25 Combine like terms: 35 + 2.25 = 37.25 2.25 + -3b + b2 = 37.25 Factor a perfect square on the left side: (b + -1.5)(b + -1.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (b + -1.5) equal to 6.103277808 and -6.103277808.Subproblem 1
b + -1.5 = 6.103277808 Simplifying b + -1.5 = 6.103277808 Reorder the terms: -1.5 + b = 6.103277808 Solving -1.5 + b = 6.103277808 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 = 6.103277808 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = 6.103277808 + 1.5 b = 6.103277808 + 1.5 Combine like terms: 6.103277808 + 1.5 = 7.603277808 b = 7.603277808 Simplifying b = 7.603277808Subproblem 2
b + -1.5 = -6.103277808 Simplifying b + -1.5 = -6.103277808 Reorder the terms: -1.5 + b = -6.103277808 Solving -1.5 + b = -6.103277808 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 = -6.103277808 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = -6.103277808 + 1.5 b = -6.103277808 + 1.5 Combine like terms: -6.103277808 + 1.5 = -4.603277808 b = -4.603277808 Simplifying b = -4.603277808Solution
The solution to the problem is based on the solutions from the subproblems. b = {7.603277808, -4.603277808}
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