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Simplifying 5b3 + 24b2 = 7b Reorder the terms: 24b2 + 5b3 = 7b Solving 24b2 + 5b3 = 7b Solving for variable 'b'. Reorder the terms: -7b + 24b2 + 5b3 = 7b + -7b Combine like terms: 7b + -7b = 0 -7b + 24b2 + 5b3 = 0 Factor out the Greatest Common Factor (GCF), 'b'. b(-7 + 24b + 5b2) = 0Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0Subproblem 2
Set the factor '(-7 + 24b + 5b2)' equal to zero and attempt to solve: Simplifying -7 + 24b + 5b2 = 0 Solving -7 + 24b + 5b2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 4.8b + b2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 4.8b + 1.4 + b2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 4.8b + b2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 4.8b + b2 = 0 + 1.4 4.8b + b2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 4.8b + b2 = 1.4 The b term is 4.8b. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8b + 5.76 + b2 = 1.4 + 5.76 Reorder the terms: 5.76 + 4.8b + b2 = 1.4 + 5.76 Combine like terms: 1.4 + 5.76 = 7.16 5.76 + 4.8b + b2 = 7.16 Factor a perfect square on the left side: (b + 2.4)(b + 2.4) = 7.16 Calculate the square root of the right side: 2.675817632 Break this problem into two subproblems by setting (b + 2.4) equal to 2.675817632 and -2.675817632.Subproblem 1
b + 2.4 = 2.675817632 Simplifying b + 2.4 = 2.675817632 Reorder the terms: 2.4 + b = 2.675817632 Solving 2.4 + b = 2.675817632 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + b = 2.675817632 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + b = 2.675817632 + -2.4 b = 2.675817632 + -2.4 Combine like terms: 2.675817632 + -2.4 = 0.275817632 b = 0.275817632 Simplifying b = 0.275817632Subproblem 2
b + 2.4 = -2.675817632 Simplifying b + 2.4 = -2.675817632 Reorder the terms: 2.4 + b = -2.675817632 Solving 2.4 + b = -2.675817632 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + b = -2.675817632 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + b = -2.675817632 + -2.4 b = -2.675817632 + -2.4 Combine like terms: -2.675817632 + -2.4 = -5.075817632 b = -5.075817632 Simplifying b = -5.075817632Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.275817632, -5.075817632}Solution
b = {0, 0.275817632, -5.075817632}
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