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Simplifying 14b2 + 5b + -4 = 0 Reorder the terms: -4 + 5b + 14b2 = 0 Solving -4 + 5b + 14b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.2857142857 + 0.3571428571b + b2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.3571428571b + 0.2857142857 + b2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 0.3571428571b + b2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 0.3571428571b + b2 = 0 + 0.2857142857 0.3571428571b + b2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 0.3571428571b + b2 = 0.2857142857 The b term is 0.3571428571b. Take half its coefficient (0.1785714286). Square it (0.03188775511) and add it to both sides. Add '0.03188775511' to each side of the equation. 0.3571428571b + 0.03188775511 + b2 = 0.2857142857 + 0.03188775511 Reorder the terms: 0.03188775511 + 0.3571428571b + b2 = 0.2857142857 + 0.03188775511 Combine like terms: 0.2857142857 + 0.03188775511 = 0.31760204081 0.03188775511 + 0.3571428571b + b2 = 0.31760204081 Factor a perfect square on the left side: (b + 0.1785714286)(b + 0.1785714286) = 0.31760204081 Calculate the square root of the right side: 0.563561923 Break this problem into two subproblems by setting (b + 0.1785714286) equal to 0.563561923 and -0.563561923.Subproblem 1
b + 0.1785714286 = 0.563561923 Simplifying b + 0.1785714286 = 0.563561923 Reorder the terms: 0.1785714286 + b = 0.563561923 Solving 0.1785714286 + b = 0.563561923 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.1785714286' to each side of the equation. 0.1785714286 + -0.1785714286 + b = 0.563561923 + -0.1785714286 Combine like terms: 0.1785714286 + -0.1785714286 = 0.0000000000 0.0000000000 + b = 0.563561923 + -0.1785714286 b = 0.563561923 + -0.1785714286 Combine like terms: 0.563561923 + -0.1785714286 = 0.3849904944 b = 0.3849904944 Simplifying b = 0.3849904944Subproblem 2
b + 0.1785714286 = -0.563561923 Simplifying b + 0.1785714286 = -0.563561923 Reorder the terms: 0.1785714286 + b = -0.563561923 Solving 0.1785714286 + b = -0.563561923 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-0.1785714286' to each side of the equation. 0.1785714286 + -0.1785714286 + b = -0.563561923 + -0.1785714286 Combine like terms: 0.1785714286 + -0.1785714286 = 0.0000000000 0.0000000000 + b = -0.563561923 + -0.1785714286 b = -0.563561923 + -0.1785714286 Combine like terms: -0.563561923 + -0.1785714286 = -0.7421333516 b = -0.7421333516 Simplifying b = -0.7421333516Solution
The solution to the problem is based on the solutions from the subproblems. b = {0.3849904944, -0.7421333516}
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