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Simplifying -4b(-3b + -5) + -5(-2b + -3) = 0 Reorder the terms: -4b(-5 + -3b) + -5(-2b + -3) = 0 (-5 * -4b + -3b * -4b) + -5(-2b + -3) = 0 (20b + 12b2) + -5(-2b + -3) = 0 Reorder the terms: 20b + 12b2 + -5(-3 + -2b) = 0 20b + 12b2 + (-3 * -5 + -2b * -5) = 0 20b + 12b2 + (15 + 10b) = 0 Reorder the terms: 15 + 20b + 10b + 12b2 = 0 Combine like terms: 20b + 10b = 30b 15 + 30b + 12b2 = 0 Solving 15 + 30b + 12b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + 10b + 4b2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 10b + 4b2)' equal to zero and attempt to solve: Simplifying 5 + 10b + 4b2 = 0 Solving 5 + 10b + 4b2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 2.5b + b2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 2.5b + -1.25 + b2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 2.5b + b2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 2.5b + b2 = 0 + -1.25 2.5b + b2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 2.5b + b2 = -1.25 The b term is 2.5b. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5b + 1.5625 + b2 = -1.25 + 1.5625 Reorder the terms: 1.5625 + 2.5b + b2 = -1.25 + 1.5625 Combine like terms: -1.25 + 1.5625 = 0.3125 1.5625 + 2.5b + b2 = 0.3125 Factor a perfect square on the left side: (b + 1.25)(b + 1.25) = 0.3125 Calculate the square root of the right side: 0.559016994 Break this problem into two subproblems by setting (b + 1.25) equal to 0.559016994 and -0.559016994.Subproblem 1
b + 1.25 = 0.559016994 Simplifying b + 1.25 = 0.559016994 Reorder the terms: 1.25 + b = 0.559016994 Solving 1.25 + b = 0.559016994 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + b = 0.559016994 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + b = 0.559016994 + -1.25 b = 0.559016994 + -1.25 Combine like terms: 0.559016994 + -1.25 = -0.690983006 b = -0.690983006 Simplifying b = -0.690983006Subproblem 2
b + 1.25 = -0.559016994 Simplifying b + 1.25 = -0.559016994 Reorder the terms: 1.25 + b = -0.559016994 Solving 1.25 + b = -0.559016994 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + b = -0.559016994 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + b = -0.559016994 + -1.25 b = -0.559016994 + -1.25 Combine like terms: -0.559016994 + -1.25 = -1.809016994 b = -1.809016994 Simplifying b = -1.809016994Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.690983006, -1.809016994}Solution
b = {-0.690983006, -1.809016994}
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