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Simplifying 4b2 + -10b = 13 Reorder the terms: -10b + 4b2 = 13 Solving -10b + 4b2 = 13 Solving for variable 'b'. Reorder the terms: -13 + -10b + 4b2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -10b + 4b2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + -2.5b + b2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + -2.5b + 3.25 + b2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + -2.5b + b2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + -2.5b + b2 = 0 + 3.25 -2.5b + b2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 -2.5b + b2 = 3.25 The b term is -2.5b. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5b + 1.5625 + b2 = 3.25 + 1.5625 Reorder the terms: 1.5625 + -2.5b + b2 = 3.25 + 1.5625 Combine like terms: 3.25 + 1.5625 = 4.8125 1.5625 + -2.5b + b2 = 4.8125 Factor a perfect square on the left side: (b + -1.25)(b + -1.25) = 4.8125 Calculate the square root of the right side: 2.193741097 Break this problem into two subproblems by setting (b + -1.25) equal to 2.193741097 and -2.193741097.Subproblem 1
b + -1.25 = 2.193741097 Simplifying b + -1.25 = 2.193741097 Reorder the terms: -1.25 + b = 2.193741097 Solving -1.25 + b = 2.193741097 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + b = 2.193741097 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + b = 2.193741097 + 1.25 b = 2.193741097 + 1.25 Combine like terms: 2.193741097 + 1.25 = 3.443741097 b = 3.443741097 Simplifying b = 3.443741097Subproblem 2
b + -1.25 = -2.193741097 Simplifying b + -1.25 = -2.193741097 Reorder the terms: -1.25 + b = -2.193741097 Solving -1.25 + b = -2.193741097 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + b = -2.193741097 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + b = -2.193741097 + 1.25 b = -2.193741097 + 1.25 Combine like terms: -2.193741097 + 1.25 = -0.943741097 b = -0.943741097 Simplifying b = -0.943741097Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.443741097, -0.943741097}
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