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Simplifying b2 + 3b + -972 = 0 Reorder the terms: -972 + 3b + b2 = 0 Solving -972 + 3b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '972' to each side of the equation. -972 + 3b + 972 + b2 = 0 + 972 Reorder the terms: -972 + 972 + 3b + b2 = 0 + 972 Combine like terms: -972 + 972 = 0 0 + 3b + b2 = 0 + 972 3b + b2 = 0 + 972 Combine like terms: 0 + 972 = 972 3b + b2 = 972 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 = 972 + 2.25 Reorder the terms: 2.25 + 3b + b2 = 972 + 2.25 Combine like terms: 972 + 2.25 = 974.25 2.25 + 3b + b2 = 974.25 Factor a perfect square on the left side: (b + 1.5)(b + 1.5) = 974.25 Calculate the square root of the right side: 31.21297807 Break this problem into two subproblems by setting (b + 1.5) equal to 31.21297807 and -31.21297807.Subproblem 1
b + 1.5 = 31.21297807 Simplifying b + 1.5 = 31.21297807 Reorder the terms: 1.5 + b = 31.21297807 Solving 1.5 + b = 31.21297807 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 = 31.21297807 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + b = 31.21297807 + -1.5 b = 31.21297807 + -1.5 Combine like terms: 31.21297807 + -1.5 = 29.71297807 b = 29.71297807 Simplifying b = 29.71297807Subproblem 2
b + 1.5 = -31.21297807 Simplifying b + 1.5 = -31.21297807 Reorder the terms: 1.5 + b = -31.21297807 Solving 1.5 + b = -31.21297807 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 = -31.21297807 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + b = -31.21297807 + -1.5 b = -31.21297807 + -1.5 Combine like terms: -31.21297807 + -1.5 = -32.71297807 b = -32.71297807 Simplifying b = -32.71297807Solution
The solution to the problem is based on the solutions from the subproblems. b = {29.71297807, -32.71297807}
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