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Simplifying 1.3b(8 + -1b) + 3.7b = -5.2 (8 * 1.3b + -1b * 1.3b) + 3.7b = -5.2 (10.4b + -1.3b2) + 3.7b = -5.2 Reorder the terms: 10.4b + 3.7b + -1.3b2 = -5.2 Combine like terms: 10.4b + 3.7b = 14.1b 14.1b + -1.3b2 = -5.2 Solving 14.1b + -1.3b2 = -5.2 Solving for variable 'b'. Reorder the terms: 5.2 + 14.1b + -1.3b2 = -5.2 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 5.2 + 14.1b + -1.3b2 = 0.0 Begin completing the square. Divide all terms by -1.3 the coefficient of the squared term: Divide each side by '-1.3'. -4 + -10.84615385b + b2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -10.84615385b + 4 + b2 = 0 + 4 Reorder the terms: -4 + 4 + -10.84615385b + b2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -10.84615385b + b2 = 0 + 4 -10.84615385b + b2 = 0 + 4 Combine like terms: 0 + 4 = 4 -10.84615385b + b2 = 4 The b term is -10.84615385b. Take half its coefficient (-5.423076925). Square it (29.40976333) and add it to both sides. Add '29.40976333' to each side of the equation. -10.84615385b + 29.40976333 + b2 = 4 + 29.40976333 Reorder the terms: 29.40976333 + -10.84615385b + b2 = 4 + 29.40976333 Combine like terms: 4 + 29.40976333 = 33.40976333 29.40976333 + -10.84615385b + b2 = 33.40976333 Factor a perfect square on the left side: (b + -5.423076925)(b + -5.423076925) = 33.40976333 Calculate the square root of the right side: 5.780117934 Break this problem into two subproblems by setting (b + -5.423076925) equal to 5.780117934 and -5.780117934.Subproblem 1
b + -5.423076925 = 5.780117934 Simplifying b + -5.423076925 = 5.780117934 Reorder the terms: -5.423076925 + b = 5.780117934 Solving -5.423076925 + b = 5.780117934 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5.423076925' to each side of the equation. -5.423076925 + 5.423076925 + b = 5.780117934 + 5.423076925 Combine like terms: -5.423076925 + 5.423076925 = 0.000000000 0.000000000 + b = 5.780117934 + 5.423076925 b = 5.780117934 + 5.423076925 Combine like terms: 5.780117934 + 5.423076925 = 11.203194859 b = 11.203194859 Simplifying b = 11.203194859Subproblem 2
b + -5.423076925 = -5.780117934 Simplifying b + -5.423076925 = -5.780117934 Reorder the terms: -5.423076925 + b = -5.780117934 Solving -5.423076925 + b = -5.780117934 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5.423076925' to each side of the equation. -5.423076925 + 5.423076925 + b = -5.780117934 + 5.423076925 Combine like terms: -5.423076925 + 5.423076925 = 0.000000000 0.000000000 + b = -5.780117934 + 5.423076925 b = -5.780117934 + 5.423076925 Combine like terms: -5.780117934 + 5.423076925 = -0.357041009 b = -0.357041009 Simplifying b = -0.357041009Solution
The solution to the problem is based on the solutions from the subproblems. b = {11.203194859, -0.357041009}
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