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Simplifying 0 = 4b2 + -200b + 16 Reorder the terms: 0 = 16 + -200b + 4b2 Solving 0 = 16 + -200b + 4b2 Solving for variable 'b'. Combine like terms: 0 + -16 = -16 -16 + 200b + -4b2 = 16 + -200b + 4b2 + -16 + 200b + -4b2 Reorder the terms: -16 + 200b + -4b2 = 16 + -16 + -200b + 200b + 4b2 + -4b2 Combine like terms: 16 + -16 = 0 -16 + 200b + -4b2 = 0 + -200b + 200b + 4b2 + -4b2 -16 + 200b + -4b2 = -200b + 200b + 4b2 + -4b2 Combine like terms: -200b + 200b = 0 -16 + 200b + -4b2 = 0 + 4b2 + -4b2 -16 + 200b + -4b2 = 4b2 + -4b2 Combine like terms: 4b2 + -4b2 = 0 -16 + 200b + -4b2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 50b + -1b2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + 50b + -1b2)' equal to zero and attempt to solve: Simplifying -4 + 50b + -1b2 = 0 Solving -4 + 50b + -1b2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -50b + b2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -50b + -4 + b2 = 0 + -4 Reorder the terms: 4 + -4 + -50b + b2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -50b + b2 = 0 + -4 -50b + b2 = 0 + -4 Combine like terms: 0 + -4 = -4 -50b + b2 = -4 The b term is -50b. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50b + 625 + b2 = -4 + 625 Reorder the terms: 625 + -50b + b2 = -4 + 625 Combine like terms: -4 + 625 = 621 625 + -50b + b2 = 621 Factor a perfect square on the left side: (b + -25)(b + -25) = 621 Calculate the square root of the right side: 24.919871589 Break this problem into two subproblems by setting (b + -25) equal to 24.919871589 and -24.919871589.Subproblem 1
b + -25 = 24.919871589 Simplifying b + -25 = 24.919871589 Reorder the terms: -25 + b = 24.919871589 Solving -25 + b = 24.919871589 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + b = 24.919871589 + 25 Combine like terms: -25 + 25 = 0 0 + b = 24.919871589 + 25 b = 24.919871589 + 25 Combine like terms: 24.919871589 + 25 = 49.919871589 b = 49.919871589 Simplifying b = 49.919871589Subproblem 2
b + -25 = -24.919871589 Simplifying b + -25 = -24.919871589 Reorder the terms: -25 + b = -24.919871589 Solving -25 + b = -24.919871589 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + b = -24.919871589 + 25 Combine like terms: -25 + 25 = 0 0 + b = -24.919871589 + 25 b = -24.919871589 + 25 Combine like terms: -24.919871589 + 25 = 0.080128411 b = 0.080128411 Simplifying b = 0.080128411Solution
The solution to the problem is based on the solutions from the subproblems. b = {49.919871589, 0.080128411}Solution
b = {49.919871589, 0.080128411}
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