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Simplifying 8b * b + -192b = -488 Multiply b * b 8b2 + -192b = -488 Reorder the terms: -192b + 8b2 = -488 Solving -192b + 8b2 = -488 Solving for variable 'b'. Reorder the terms: 488 + -192b + 8b2 = -488 + 488 Combine like terms: -488 + 488 = 0 488 + -192b + 8b2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(61 + -24b + b2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(61 + -24b + b2)' equal to zero and attempt to solve: Simplifying 61 + -24b + b2 = 0 Solving 61 + -24b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '-61' to each side of the equation. 61 + -24b + -61 + b2 = 0 + -61 Reorder the terms: 61 + -61 + -24b + b2 = 0 + -61 Combine like terms: 61 + -61 = 0 0 + -24b + b2 = 0 + -61 -24b + b2 = 0 + -61 Combine like terms: 0 + -61 = -61 -24b + b2 = -61 The b term is -24b. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24b + 144 + b2 = -61 + 144 Reorder the terms: 144 + -24b + b2 = -61 + 144 Combine like terms: -61 + 144 = 83 144 + -24b + b2 = 83 Factor a perfect square on the left side: (b + -12)(b + -12) = 83 Calculate the square root of the right side: 9.110433579 Break this problem into two subproblems by setting (b + -12) equal to 9.110433579 and -9.110433579.Subproblem 1
b + -12 = 9.110433579 Simplifying b + -12 = 9.110433579 Reorder the terms: -12 + b = 9.110433579 Solving -12 + b = 9.110433579 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + b = 9.110433579 + 12 Combine like terms: -12 + 12 = 0 0 + b = 9.110433579 + 12 b = 9.110433579 + 12 Combine like terms: 9.110433579 + 12 = 21.110433579 b = 21.110433579 Simplifying b = 21.110433579Subproblem 2
b + -12 = -9.110433579 Simplifying b + -12 = -9.110433579 Reorder the terms: -12 + b = -9.110433579 Solving -12 + b = -9.110433579 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + b = -9.110433579 + 12 Combine like terms: -12 + 12 = 0 0 + b = -9.110433579 + 12 b = -9.110433579 + 12 Combine like terms: -9.110433579 + 12 = 2.889566421 b = 2.889566421 Simplifying b = 2.889566421Solution
The solution to the problem is based on the solutions from the subproblems. b = {21.110433579, 2.889566421}Solution
b = {21.110433579, 2.889566421}
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