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Simplifying 28b2 + -208b + -132 = 0 Reorder the terms: -132 + -208b + 28b2 = 0 Solving -132 + -208b + 28b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '4'. 4(-33 + -52b + 7b2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-33 + -52b + 7b2)' equal to zero and attempt to solve: Simplifying -33 + -52b + 7b2 = 0 Solving -33 + -52b + 7b2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.714285714 + -7.428571429b + b2 = 0 Move the constant term to the right: Add '4.714285714' to each side of the equation. -4.714285714 + -7.428571429b + 4.714285714 + b2 = 0 + 4.714285714 Reorder the terms: -4.714285714 + 4.714285714 + -7.428571429b + b2 = 0 + 4.714285714 Combine like terms: -4.714285714 + 4.714285714 = 0.000000000 0.000000000 + -7.428571429b + b2 = 0 + 4.714285714 -7.428571429b + b2 = 0 + 4.714285714 Combine like terms: 0 + 4.714285714 = 4.714285714 -7.428571429b + b2 = 4.714285714 The b term is -7.428571429b. Take half its coefficient (-3.714285715). Square it (13.79591837) and add it to both sides. Add '13.79591837' to each side of the equation. -7.428571429b + 13.79591837 + b2 = 4.714285714 + 13.79591837 Reorder the terms: 13.79591837 + -7.428571429b + b2 = 4.714285714 + 13.79591837 Combine like terms: 4.714285714 + 13.79591837 = 18.510204084 13.79591837 + -7.428571429b + b2 = 18.510204084 Factor a perfect square on the left side: (b + -3.714285715)(b + -3.714285715) = 18.510204084 Calculate the square root of the right side: 4.302348671 Break this problem into two subproblems by setting (b + -3.714285715) equal to 4.302348671 and -4.302348671.Subproblem 1
b + -3.714285715 = 4.302348671 Simplifying b + -3.714285715 = 4.302348671 Reorder the terms: -3.714285715 + b = 4.302348671 Solving -3.714285715 + b = 4.302348671 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.714285715' to each side of the equation. -3.714285715 + 3.714285715 + b = 4.302348671 + 3.714285715 Combine like terms: -3.714285715 + 3.714285715 = 0.000000000 0.000000000 + b = 4.302348671 + 3.714285715 b = 4.302348671 + 3.714285715 Combine like terms: 4.302348671 + 3.714285715 = 8.016634386 b = 8.016634386 Simplifying b = 8.016634386Subproblem 2
b + -3.714285715 = -4.302348671 Simplifying b + -3.714285715 = -4.302348671 Reorder the terms: -3.714285715 + b = -4.302348671 Solving -3.714285715 + b = -4.302348671 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.714285715' to each side of the equation. -3.714285715 + 3.714285715 + b = -4.302348671 + 3.714285715 Combine like terms: -3.714285715 + 3.714285715 = 0.000000000 0.000000000 + b = -4.302348671 + 3.714285715 b = -4.302348671 + 3.714285715 Combine like terms: -4.302348671 + 3.714285715 = -0.588062956 b = -0.588062956 Simplifying b = -0.588062956Solution
The solution to the problem is based on the solutions from the subproblems. b = {8.016634386, -0.588062956}Solution
b = {8.016634386, -0.588062956}
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