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Simplifying 0 = 4b2 + -96b + 16 Reorder the terms: 0 = 16 + -96b + 4b2 Solving 0 = 16 + -96b + 4b2 Solving for variable 'b'. Combine like terms: 0 + -16 = -16 -16 + 96b + -4b2 = 16 + -96b + 4b2 + -16 + 96b + -4b2 Reorder the terms: -16 + 96b + -4b2 = 16 + -16 + -96b + 96b + 4b2 + -4b2 Combine like terms: 16 + -16 = 0 -16 + 96b + -4b2 = 0 + -96b + 96b + 4b2 + -4b2 -16 + 96b + -4b2 = -96b + 96b + 4b2 + -4b2 Combine like terms: -96b + 96b = 0 -16 + 96b + -4b2 = 0 + 4b2 + -4b2 -16 + 96b + -4b2 = 4b2 + -4b2 Combine like terms: 4b2 + -4b2 = 0 -16 + 96b + -4b2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 24b + -1b2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + 24b + -1b2)' equal to zero and attempt to solve: Simplifying -4 + 24b + -1b2 = 0 Solving -4 + 24b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -24b + b2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -24b + -4 + b2 = 0 + -4 Reorder the terms: 4 + -4 + -24b + b2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -24b + b2 = 0 + -4 -24b + b2 = 0 + -4 Combine like terms: 0 + -4 = -4 -24b + b2 = -4 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 = -4 + 144 Reorder the terms: 144 + -24b + b2 = -4 + 144 Combine like terms: -4 + 144 = 140 144 + -24b + b2 = 140 Factor a perfect square on the left side: (b + -12)(b + -12) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (b + -12) equal to 11.832159566 and -11.832159566.Subproblem 1
b + -12 = 11.832159566 Simplifying b + -12 = 11.832159566 Reorder the terms: -12 + b = 11.832159566 Solving -12 + b = 11.832159566 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 = 11.832159566 + 12 Combine like terms: -12 + 12 = 0 0 + b = 11.832159566 + 12 b = 11.832159566 + 12 Combine like terms: 11.832159566 + 12 = 23.832159566 b = 23.832159566 Simplifying b = 23.832159566Subproblem 2
b + -12 = -11.832159566 Simplifying b + -12 = -11.832159566 Reorder the terms: -12 + b = -11.832159566 Solving -12 + b = -11.832159566 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 = -11.832159566 + 12 Combine like terms: -12 + 12 = 0 0 + b = -11.832159566 + 12 b = -11.832159566 + 12 Combine like terms: -11.832159566 + 12 = 0.167840434 b = 0.167840434 Simplifying b = 0.167840434Solution
The solution to the problem is based on the solutions from the subproblems. b = {23.832159566, 0.167840434}Solution
b = {23.832159566, 0.167840434}
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