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Simplifying 2b2 + 9b + -7 = 0 Reorder the terms: -7 + 9b + 2b2 = 0 Solving -7 + 9b + 2b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 4.5b + b2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 4.5b + 3.5 + b2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 4.5b + b2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 4.5b + b2 = 0 + 3.5 4.5b + b2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 4.5b + b2 = 3.5 The b term is 4.5b. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5b + 5.0625 + b2 = 3.5 + 5.0625 Reorder the terms: 5.0625 + 4.5b + b2 = 3.5 + 5.0625 Combine like terms: 3.5 + 5.0625 = 8.5625 5.0625 + 4.5b + b2 = 8.5625 Factor a perfect square on the left side: (b + 2.25)(b + 2.25) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (b + 2.25) equal to 2.926174978 and -2.926174978.Subproblem 1
b + 2.25 = 2.926174978 Simplifying b + 2.25 = 2.926174978 Reorder the terms: 2.25 + b = 2.926174978 Solving 2.25 + b = 2.926174978 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + b = 2.926174978 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + b = 2.926174978 + -2.25 b = 2.926174978 + -2.25 Combine like terms: 2.926174978 + -2.25 = 0.676174978 b = 0.676174978 Simplifying b = 0.676174978Subproblem 2
b + 2.25 = -2.926174978 Simplifying b + 2.25 = -2.926174978 Reorder the terms: 2.25 + b = -2.926174978 Solving 2.25 + b = -2.926174978 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + b = -2.926174978 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + b = -2.926174978 + -2.25 b = -2.926174978 + -2.25 Combine like terms: -2.926174978 + -2.25 = -5.176174978 b = -5.176174978 Simplifying b = -5.176174978Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.676174978, -5.176174978}
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