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Simplifying b2 + -13b + 4 = -3 Reorder the terms: 4 + -13b + b2 = -3 Solving 4 + -13b + b2 = -3 Solving for variable 'b'. Reorder the terms: 4 + 3 + -13b + b2 = -3 + 3 Combine like terms: 4 + 3 = 7 7 + -13b + b2 = -3 + 3 Combine like terms: -3 + 3 = 0 7 + -13b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -13b + -7 + b2 = 0 + -7 Reorder the terms: 7 + -7 + -13b + b2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -13b + b2 = 0 + -7 -13b + b2 = 0 + -7 Combine like terms: 0 + -7 = -7 -13b + b2 = -7 The b term is -13b. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13b + 42.25 + b2 = -7 + 42.25 Reorder the terms: 42.25 + -13b + b2 = -7 + 42.25 Combine like terms: -7 + 42.25 = 35.25 42.25 + -13b + b2 = 35.25 Factor a perfect square on the left side: (b + -6.5)(b + -6.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (b + -6.5) equal to 5.937171044 and -5.937171044.Subproblem 1
b + -6.5 = 5.937171044 Simplifying b + -6.5 = 5.937171044 Reorder the terms: -6.5 + b = 5.937171044 Solving -6.5 + b = 5.937171044 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + b = 5.937171044 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + b = 5.937171044 + 6.5 b = 5.937171044 + 6.5 Combine like terms: 5.937171044 + 6.5 = 12.437171044 b = 12.437171044 Simplifying b = 12.437171044Subproblem 2
b + -6.5 = -5.937171044 Simplifying b + -6.5 = -5.937171044 Reorder the terms: -6.5 + b = -5.937171044 Solving -6.5 + b = -5.937171044 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + b = -5.937171044 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + b = -5.937171044 + 6.5 b = -5.937171044 + 6.5 Combine like terms: -5.937171044 + 6.5 = 0.562828956 b = 0.562828956 Simplifying b = 0.562828956Solution
The solution to the problem is based on the solutions from the subproblems. b = {12.437171044, 0.562828956}
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