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Simplifying 9 + -2b(b + 3) = 4b Reorder the terms: 9 + -2b(3 + b) = 4b 9 + (3 * -2b + b * -2b) = 4b 9 + (-6b + -2b2) = 4b Solving 9 + -6b + -2b2 = 4b Solving for variable 'b'. Reorder the terms: 9 + -6b + -4b + -2b2 = 4b + -4b Combine like terms: -6b + -4b = -10b 9 + -10b + -2b2 = 4b + -4b Combine like terms: 4b + -4b = 0 9 + -10b + -2b2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4.5 + 5b + b2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 5b + 4.5 + b2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 5b + b2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 5b + b2 = 0 + 4.5 5b + b2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 5b + b2 = 4.5 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 = 4.5 + 6.25 Reorder the terms: 6.25 + 5b + b2 = 4.5 + 6.25 Combine like terms: 4.5 + 6.25 = 10.75 6.25 + 5b + b2 = 10.75 Factor a perfect square on the left side: (b + 2.5)(b + 2.5) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (b + 2.5) equal to 3.278719262 and -3.278719262.Subproblem 1
b + 2.5 = 3.278719262 Simplifying b + 2.5 = 3.278719262 Reorder the terms: 2.5 + b = 3.278719262 Solving 2.5 + b = 3.278719262 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 = 3.278719262 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = 3.278719262 + -2.5 b = 3.278719262 + -2.5 Combine like terms: 3.278719262 + -2.5 = 0.778719262 b = 0.778719262 Simplifying b = 0.778719262Subproblem 2
b + 2.5 = -3.278719262 Simplifying b + 2.5 = -3.278719262 Reorder the terms: 2.5 + b = -3.278719262 Solving 2.5 + b = -3.278719262 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 = -3.278719262 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = -3.278719262 + -2.5 b = -3.278719262 + -2.5 Combine like terms: -3.278719262 + -2.5 = -5.778719262 b = -5.778719262 Simplifying b = -5.778719262Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.778719262, -5.778719262}
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