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Simplifying 2b2 + -3b + -30 = 0 Reorder the terms: -30 + -3b + 2b2 = 0 Solving -30 + -3b + 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'. -15 + -1.5b + b2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -1.5b + 15 + b2 = 0 + 15 Reorder the terms: -15 + 15 + -1.5b + b2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1.5b + b2 = 0 + 15 -1.5b + b2 = 0 + 15 Combine like terms: 0 + 15 = 15 -1.5b + b2 = 15 The b term is -1.5b. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5b + 0.5625 + b2 = 15 + 0.5625 Reorder the terms: 0.5625 + -1.5b + b2 = 15 + 0.5625 Combine like terms: 15 + 0.5625 = 15.5625 0.5625 + -1.5b + b2 = 15.5625 Factor a perfect square on the left side: (b + -0.75)(b + -0.75) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (b + -0.75) equal to 3.94493346 and -3.94493346.Subproblem 1
b + -0.75 = 3.94493346 Simplifying b + -0.75 = 3.94493346 Reorder the terms: -0.75 + b = 3.94493346 Solving -0.75 + b = 3.94493346 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + b = 3.94493346 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + b = 3.94493346 + 0.75 b = 3.94493346 + 0.75 Combine like terms: 3.94493346 + 0.75 = 4.69493346 b = 4.69493346 Simplifying b = 4.69493346Subproblem 2
b + -0.75 = -3.94493346 Simplifying b + -0.75 = -3.94493346 Reorder the terms: -0.75 + b = -3.94493346 Solving -0.75 + b = -3.94493346 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + b = -3.94493346 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + b = -3.94493346 + 0.75 b = -3.94493346 + 0.75 Combine like terms: -3.94493346 + 0.75 = -3.19493346 b = -3.19493346 Simplifying b = -3.19493346Solution
The solution to the problem is based on the solutions from the subproblems. b = {4.69493346, -3.19493346}
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