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Simplifying b2 + -2.3b + -1.2 = 0 Reorder the terms: -1.2 + -2.3b + b2 = 0 Solving -1.2 + -2.3b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -2.3b + 1.2 + b2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -2.3b + b2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -2.3b + b2 = 0 + 1.2 -2.3b + b2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -2.3b + b2 = 1.2 The b term is -2.3b. Take half its coefficient (-1.15). Square it (1.3225) and add it to both sides. Add '1.3225' to each side of the equation. -2.3b + 1.3225 + b2 = 1.2 + 1.3225 Reorder the terms: 1.3225 + -2.3b + b2 = 1.2 + 1.3225 Combine like terms: 1.2 + 1.3225 = 2.5225 1.3225 + -2.3b + b2 = 2.5225 Factor a perfect square on the left side: (b + -1.15)(b + -1.15) = 2.5225 Calculate the square root of the right side: 1.588238017 Break this problem into two subproblems by setting (b + -1.15) equal to 1.588238017 and -1.588238017.Subproblem 1
b + -1.15 = 1.588238017 Simplifying b + -1.15 = 1.588238017 Reorder the terms: -1.15 + b = 1.588238017 Solving -1.15 + b = 1.588238017 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + b = 1.588238017 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + b = 1.588238017 + 1.15 b = 1.588238017 + 1.15 Combine like terms: 1.588238017 + 1.15 = 2.738238017 b = 2.738238017 Simplifying b = 2.738238017Subproblem 2
b + -1.15 = -1.588238017 Simplifying b + -1.15 = -1.588238017 Reorder the terms: -1.15 + b = -1.588238017 Solving -1.15 + b = -1.588238017 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + b = -1.588238017 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + b = -1.588238017 + 1.15 b = -1.588238017 + 1.15 Combine like terms: -1.588238017 + 1.15 = -0.438238017 b = -0.438238017 Simplifying b = -0.438238017Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.738238017, -0.438238017}
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