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Simplifying 0 = 4b2 + -76b + 16 Reorder the terms: 0 = 16 + -76b + 4b2 Solving 0 = 16 + -76b + 4b2 Solving for variable 'b'. Combine like terms: 0 + -16 = -16 -16 + 76b + -4b2 = 16 + -76b + 4b2 + -16 + 76b + -4b2 Reorder the terms: -16 + 76b + -4b2 = 16 + -16 + -76b + 76b + 4b2 + -4b2 Combine like terms: 16 + -16 = 0 -16 + 76b + -4b2 = 0 + -76b + 76b + 4b2 + -4b2 -16 + 76b + -4b2 = -76b + 76b + 4b2 + -4b2 Combine like terms: -76b + 76b = 0 -16 + 76b + -4b2 = 0 + 4b2 + -4b2 -16 + 76b + -4b2 = 4b2 + -4b2 Combine like terms: 4b2 + -4b2 = 0 -16 + 76b + -4b2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 19b + -1b2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + 19b + -1b2)' equal to zero and attempt to solve: Simplifying -4 + 19b + -1b2 = 0 Solving -4 + 19b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -19b + b2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -19b + -4 + b2 = 0 + -4 Reorder the terms: 4 + -4 + -19b + b2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -19b + b2 = 0 + -4 -19b + b2 = 0 + -4 Combine like terms: 0 + -4 = -4 -19b + b2 = -4 The b term is -19b. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19b + 90.25 + b2 = -4 + 90.25 Reorder the terms: 90.25 + -19b + b2 = -4 + 90.25 Combine like terms: -4 + 90.25 = 86.25 90.25 + -19b + b2 = 86.25 Factor a perfect square on the left side: (b + -9.5)(b + -9.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (b + -9.5) equal to 9.287087811 and -9.287087811.Subproblem 1
b + -9.5 = 9.287087811 Simplifying b + -9.5 = 9.287087811 Reorder the terms: -9.5 + b = 9.287087811 Solving -9.5 + b = 9.287087811 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + b = 9.287087811 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + b = 9.287087811 + 9.5 b = 9.287087811 + 9.5 Combine like terms: 9.287087811 + 9.5 = 18.787087811 b = 18.787087811 Simplifying b = 18.787087811Subproblem 2
b + -9.5 = -9.287087811 Simplifying b + -9.5 = -9.287087811 Reorder the terms: -9.5 + b = -9.287087811 Solving -9.5 + b = -9.287087811 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + b = -9.287087811 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + b = -9.287087811 + 9.5 b = -9.287087811 + 9.5 Combine like terms: -9.287087811 + 9.5 = 0.212912189 b = 0.212912189 Simplifying b = 0.212912189Solution
The solution to the problem is based on the solutions from the subproblems. b = {18.787087811, 0.212912189}Solution
b = {18.787087811, 0.212912189}
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