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Simplifying 8b2 + 10b + -13 = 0 Reorder the terms: -13 + 10b + 8b2 = 0 Solving -13 + 10b + 8b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.625 + 1.25b + b2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 1.25b + 1.625 + b2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + 1.25b + b2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 1.25b + b2 = 0 + 1.625 1.25b + b2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 1.25b + b2 = 1.625 The b term is 1.25b. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25b + 0.390625 + b2 = 1.625 + 0.390625 Reorder the terms: 0.390625 + 1.25b + b2 = 1.625 + 0.390625 Combine like terms: 1.625 + 0.390625 = 2.015625 0.390625 + 1.25b + b2 = 2.015625 Factor a perfect square on the left side: (b + 0.625)(b + 0.625) = 2.015625 Calculate the square root of the right side: 1.419727086 Break this problem into two subproblems by setting (b + 0.625) equal to 1.419727086 and -1.419727086.Subproblem 1
b + 0.625 = 1.419727086 Simplifying b + 0.625 = 1.419727086 Reorder the terms: 0.625 + b = 1.419727086 Solving 0.625 + b = 1.419727086 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + b = 1.419727086 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + b = 1.419727086 + -0.625 b = 1.419727086 + -0.625 Combine like terms: 1.419727086 + -0.625 = 0.794727086 b = 0.794727086 Simplifying b = 0.794727086Subproblem 2
b + 0.625 = -1.419727086 Simplifying b + 0.625 = -1.419727086 Reorder the terms: 0.625 + b = -1.419727086 Solving 0.625 + b = -1.419727086 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + b = -1.419727086 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + b = -1.419727086 + -0.625 b = -1.419727086 + -0.625 Combine like terms: -1.419727086 + -0.625 = -2.044727086 b = -2.044727086 Simplifying b = -2.044727086Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.794727086, -2.044727086}
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