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Simplifying 5b2 + -42b + 59 = 0 Reorder the terms: 59 + -42b + 5b2 = 0 Solving 59 + -42b + 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'. 11.8 + -8.4b + b2 = 0 Move the constant term to the right: Add '-11.8' to each side of the equation. 11.8 + -8.4b + -11.8 + b2 = 0 + -11.8 Reorder the terms: 11.8 + -11.8 + -8.4b + b2 = 0 + -11.8 Combine like terms: 11.8 + -11.8 = 0.0 0.0 + -8.4b + b2 = 0 + -11.8 -8.4b + b2 = 0 + -11.8 Combine like terms: 0 + -11.8 = -11.8 -8.4b + b2 = -11.8 The b term is -8.4b. Take half its coefficient (-4.2). Square it (17.64) and add it to both sides. Add '17.64' to each side of the equation. -8.4b + 17.64 + b2 = -11.8 + 17.64 Reorder the terms: 17.64 + -8.4b + b2 = -11.8 + 17.64 Combine like terms: -11.8 + 17.64 = 5.84 17.64 + -8.4b + b2 = 5.84 Factor a perfect square on the left side: (b + -4.2)(b + -4.2) = 5.84 Calculate the square root of the right side: 2.416609195 Break this problem into two subproblems by setting (b + -4.2) equal to 2.416609195 and -2.416609195.Subproblem 1
b + -4.2 = 2.416609195 Simplifying b + -4.2 = 2.416609195 Reorder the terms: -4.2 + b = 2.416609195 Solving -4.2 + b = 2.416609195 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4.2' to each side of the equation. -4.2 + 4.2 + b = 2.416609195 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + b = 2.416609195 + 4.2 b = 2.416609195 + 4.2 Combine like terms: 2.416609195 + 4.2 = 6.616609195 b = 6.616609195 Simplifying b = 6.616609195Subproblem 2
b + -4.2 = -2.416609195 Simplifying b + -4.2 = -2.416609195 Reorder the terms: -4.2 + b = -2.416609195 Solving -4.2 + b = -2.416609195 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '4.2' to each side of the equation. -4.2 + 4.2 + b = -2.416609195 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + b = -2.416609195 + 4.2 b = -2.416609195 + 4.2 Combine like terms: -2.416609195 + 4.2 = 1.783390805 b = 1.783390805 Simplifying b = 1.783390805Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.616609195, 1.783390805}
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