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Simplifying 4b2 + 9b + -25 = 0 Reorder the terms: -25 + 9b + 4b2 = 0 Solving -25 + 9b + 4b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + 2.25b + b2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 2.25b + 6.25 + b2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 2.25b + b2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 2.25b + b2 = 0 + 6.25 2.25b + b2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 2.25b + b2 = 6.25 The b term is 2.25b. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25b + 1.265625 + b2 = 6.25 + 1.265625 Reorder the terms: 1.265625 + 2.25b + b2 = 6.25 + 1.265625 Combine like terms: 6.25 + 1.265625 = 7.515625 1.265625 + 2.25b + b2 = 7.515625 Factor a perfect square on the left side: (b + 1.125)(b + 1.125) = 7.515625 Calculate the square root of the right side: 2.741464025 Break this problem into two subproblems by setting (b + 1.125) equal to 2.741464025 and -2.741464025.Subproblem 1
b + 1.125 = 2.741464025 Simplifying b + 1.125 = 2.741464025 Reorder the terms: 1.125 + b = 2.741464025 Solving 1.125 + b = 2.741464025 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + b = 2.741464025 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + b = 2.741464025 + -1.125 b = 2.741464025 + -1.125 Combine like terms: 2.741464025 + -1.125 = 1.616464025 b = 1.616464025 Simplifying b = 1.616464025Subproblem 2
b + 1.125 = -2.741464025 Simplifying b + 1.125 = -2.741464025 Reorder the terms: 1.125 + b = -2.741464025 Solving 1.125 + b = -2.741464025 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + b = -2.741464025 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + b = -2.741464025 + -1.125 b = -2.741464025 + -1.125 Combine like terms: -2.741464025 + -1.125 = -3.866464025 b = -3.866464025 Simplifying b = -3.866464025Solution
The solution to the problem is based on the solutions from the subproblems. b = {1.616464025, -3.866464025}
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