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Simplifying -2b(b + 5) = -6 Reorder the terms: -2b(5 + b) = -6 (5 * -2b + b * -2b) = -6 (-10b + -2b2) = -6 Solving -10b + -2b2 = -6 Solving for variable 'b'. Reorder the terms: 6 + -10b + -2b2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + -10b + -2b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -5b + -1b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -5b + -1b2)' equal to zero and attempt to solve: Simplifying 3 + -5b + -1b2 = 0 Solving 3 + -5b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 5b + b2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 5b + 3 + b2 = 0 + 3 Reorder the terms: -3 + 3 + 5b + b2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 5b + b2 = 0 + 3 5b + b2 = 0 + 3 Combine like terms: 0 + 3 = 3 5b + b2 = 3 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 = 3 + 6.25 Reorder the terms: 6.25 + 5b + b2 = 3 + 6.25 Combine like terms: 3 + 6.25 = 9.25 6.25 + 5b + b2 = 9.25 Factor a perfect square on the left side: (b + 2.5)(b + 2.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (b + 2.5) equal to 3.041381265 and -3.041381265.Subproblem 1
b + 2.5 = 3.041381265 Simplifying b + 2.5 = 3.041381265 Reorder the terms: 2.5 + b = 3.041381265 Solving 2.5 + b = 3.041381265 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 = 3.041381265 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = 3.041381265 + -2.5 b = 3.041381265 + -2.5 Combine like terms: 3.041381265 + -2.5 = 0.541381265 b = 0.541381265 Simplifying b = 0.541381265Subproblem 2
b + 2.5 = -3.041381265 Simplifying b + 2.5 = -3.041381265 Reorder the terms: 2.5 + b = -3.041381265 Solving 2.5 + b = -3.041381265 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 = -3.041381265 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = -3.041381265 + -2.5 b = -3.041381265 + -2.5 Combine like terms: -3.041381265 + -2.5 = -5.541381265 b = -5.541381265 Simplifying b = -5.541381265Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.541381265, -5.541381265}Solution
b = {0.541381265, -5.541381265}
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