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Simplifying b2 + 5b + -21 = 0 Reorder the terms: -21 + 5b + b2 = 0 Solving -21 + 5b + b2 = 0 Solving for variable 'b'. Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 5b + 21 + b2 = 0 + 21 Reorder the terms: -21 + 21 + 5b + b2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 5b + b2 = 0 + 21 5b + b2 = 0 + 21 Combine like terms: 0 + 21 = 21 5b + b2 = 21 The b term is 5b. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5b + 6.25 + b2 = 21 + 6.25 Reorder the terms: 6.25 + 5b + b2 = 21 + 6.25 Combine like terms: 21 + 6.25 = 27.25 6.25 + 5b + b2 = 27.25 Factor a perfect square on the left side: (b + 2.5)(b + 2.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (b + 2.5) equal to 5.220153254 and -5.220153254.Subproblem 1
b + 2.5 = 5.220153254 Simplifying b + 2.5 = 5.220153254 Reorder the terms: 2.5 + b = 5.220153254 Solving 2.5 + b = 5.220153254 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + b = 5.220153254 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = 5.220153254 + -2.5 b = 5.220153254 + -2.5 Combine like terms: 5.220153254 + -2.5 = 2.720153254 b = 2.720153254 Simplifying b = 2.720153254Subproblem 2
b + 2.5 = -5.220153254 Simplifying b + 2.5 = -5.220153254 Reorder the terms: 2.5 + b = -5.220153254 Solving 2.5 + b = -5.220153254 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + b = -5.220153254 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = -5.220153254 + -2.5 b = -5.220153254 + -2.5 Combine like terms: -5.220153254 + -2.5 = -7.720153254 b = -7.720153254 Simplifying b = -7.720153254Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.720153254, -7.720153254}
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