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Simplifying 2b2 + -15b + 20 = 0 Reorder the terms: 20 + -15b + 2b2 = 0 Solving 20 + -15b + 2b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10 + -7.5b + b2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -7.5b + -10 + b2 = 0 + -10 Reorder the terms: 10 + -10 + -7.5b + b2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -7.5b + b2 = 0 + -10 -7.5b + b2 = 0 + -10 Combine like terms: 0 + -10 = -10 -7.5b + b2 = -10 The b term is -7.5b. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5b + 14.0625 + b2 = -10 + 14.0625 Reorder the terms: 14.0625 + -7.5b + b2 = -10 + 14.0625 Combine like terms: -10 + 14.0625 = 4.0625 14.0625 + -7.5b + b2 = 4.0625 Factor a perfect square on the left side: (b + -3.75)(b + -3.75) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (b + -3.75) equal to 2.015564437 and -2.015564437.Subproblem 1
b + -3.75 = 2.015564437 Simplifying b + -3.75 = 2.015564437 Reorder the terms: -3.75 + b = 2.015564437 Solving -3.75 + b = 2.015564437 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + b = 2.015564437 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + b = 2.015564437 + 3.75 b = 2.015564437 + 3.75 Combine like terms: 2.015564437 + 3.75 = 5.765564437 b = 5.765564437 Simplifying b = 5.765564437Subproblem 2
b + -3.75 = -2.015564437 Simplifying b + -3.75 = -2.015564437 Reorder the terms: -3.75 + b = -2.015564437 Solving -3.75 + b = -2.015564437 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + b = -2.015564437 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + b = -2.015564437 + 3.75 b = -2.015564437 + 3.75 Combine like terms: -2.015564437 + 3.75 = 1.734435563 b = 1.734435563 Simplifying b = 1.734435563Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.765564437, 1.734435563}
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