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Simplifying 5b2 + -7b + -42 = 0 Reorder the terms: -42 + -7b + 5b2 = 0 Solving -42 + -7b + 5b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8.4 + -1.4b + b2 = 0 Move the constant term to the right: Add '8.4' to each side of the equation. -8.4 + -1.4b + 8.4 + b2 = 0 + 8.4 Reorder the terms: -8.4 + 8.4 + -1.4b + b2 = 0 + 8.4 Combine like terms: -8.4 + 8.4 = 0.0 0.0 + -1.4b + b2 = 0 + 8.4 -1.4b + b2 = 0 + 8.4 Combine like terms: 0 + 8.4 = 8.4 -1.4b + b2 = 8.4 The b term is -1.4b. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4b + 0.49 + b2 = 8.4 + 0.49 Reorder the terms: 0.49 + -1.4b + b2 = 8.4 + 0.49 Combine like terms: 8.4 + 0.49 = 8.89 0.49 + -1.4b + b2 = 8.89 Factor a perfect square on the left side: (b + -0.7)(b + -0.7) = 8.89 Calculate the square root of the right side: 2.981610303 Break this problem into two subproblems by setting (b + -0.7) equal to 2.981610303 and -2.981610303.Subproblem 1
b + -0.7 = 2.981610303 Simplifying b + -0.7 = 2.981610303 Reorder the terms: -0.7 + b = 2.981610303 Solving -0.7 + b = 2.981610303 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + b = 2.981610303 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + b = 2.981610303 + 0.7 b = 2.981610303 + 0.7 Combine like terms: 2.981610303 + 0.7 = 3.681610303 b = 3.681610303 Simplifying b = 3.681610303Subproblem 2
b + -0.7 = -2.981610303 Simplifying b + -0.7 = -2.981610303 Reorder the terms: -0.7 + b = -2.981610303 Solving -0.7 + b = -2.981610303 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + b = -2.981610303 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + b = -2.981610303 + 0.7 b = -2.981610303 + 0.7 Combine like terms: -2.981610303 + 0.7 = -2.281610303 b = -2.281610303 Simplifying b = -2.281610303Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.681610303, -2.281610303}
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