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Simplifying 5b2 + -1b + -24 = 0 Reorder the terms: -24 + -1b + 5b2 = 0 Solving -24 + -1b + 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'. -4.8 + -0.2b + b2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -0.2b + 4.8 + b2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -0.2b + b2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -0.2b + b2 = 0 + 4.8 -0.2b + b2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -0.2b + b2 = 4.8 The b term is -0.2b. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2b + 0.01 + b2 = 4.8 + 0.01 Reorder the terms: 0.01 + -0.2b + b2 = 4.8 + 0.01 Combine like terms: 4.8 + 0.01 = 4.81 0.01 + -0.2b + b2 = 4.81 Factor a perfect square on the left side: (b + -0.1)(b + -0.1) = 4.81 Calculate the square root of the right side: 2.19317122 Break this problem into two subproblems by setting (b + -0.1) equal to 2.19317122 and -2.19317122.Subproblem 1
b + -0.1 = 2.19317122 Simplifying b + -0.1 = 2.19317122 Reorder the terms: -0.1 + b = 2.19317122 Solving -0.1 + b = 2.19317122 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + b = 2.19317122 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + b = 2.19317122 + 0.1 b = 2.19317122 + 0.1 Combine like terms: 2.19317122 + 0.1 = 2.29317122 b = 2.29317122 Simplifying b = 2.29317122Subproblem 2
b + -0.1 = -2.19317122 Simplifying b + -0.1 = -2.19317122 Reorder the terms: -0.1 + b = -2.19317122 Solving -0.1 + b = -2.19317122 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + b = -2.19317122 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + b = -2.19317122 + 0.1 b = -2.19317122 + 0.1 Combine like terms: -2.19317122 + 0.1 = -2.09317122 b = -2.09317122 Simplifying b = -2.09317122Solution
The solution to the problem is based on the solutions from the subproblems. b = {2.29317122, -2.09317122}
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