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Simplifying 7b2 + -4b + -56 = 0 Reorder the terms: -56 + -4b + 7b2 = 0 Solving -56 + -4b + 7b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -8 + -0.5714285714b + b2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -0.5714285714b + 8 + b2 = 0 + 8 Reorder the terms: -8 + 8 + -0.5714285714b + b2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -0.5714285714b + b2 = 0 + 8 -0.5714285714b + b2 = 0 + 8 Combine like terms: 0 + 8 = 8 -0.5714285714b + b2 = 8 The b term is -0.5714285714b. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714b + 0.08163265305 + b2 = 8 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714b + b2 = 8 + 0.08163265305 Combine like terms: 8 + 0.08163265305 = 8.08163265305 0.08163265305 + -0.5714285714b + b2 = 8.08163265305 Factor a perfect square on the left side: (b + -0.2857142857)(b + -0.2857142857) = 8.08163265305 Calculate the square root of the right side: 2.842821249 Break this problem into two subproblems by setting (b + -0.2857142857) equal to 2.842821249 and -2.842821249.Subproblem 1
b + -0.2857142857 = 2.842821249 Simplifying b + -0.2857142857 = 2.842821249 Reorder the terms: -0.2857142857 + b = 2.842821249 Solving -0.2857142857 + b = 2.842821249 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + b = 2.842821249 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + b = 2.842821249 + 0.2857142857 b = 2.842821249 + 0.2857142857 Combine like terms: 2.842821249 + 0.2857142857 = 3.1285355347 b = 3.1285355347 Simplifying b = 3.1285355347Subproblem 2
b + -0.2857142857 = -2.842821249 Simplifying b + -0.2857142857 = -2.842821249 Reorder the terms: -0.2857142857 + b = -2.842821249 Solving -0.2857142857 + b = -2.842821249 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + b = -2.842821249 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + b = -2.842821249 + 0.2857142857 b = -2.842821249 + 0.2857142857 Combine like terms: -2.842821249 + 0.2857142857 = -2.5571069633 b = -2.5571069633 Simplifying b = -2.5571069633Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.1285355347, -2.5571069633}
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