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Simplifying 4b2 + -12b + -9 = 0 Reorder the terms: -9 + -12b + 4b2 = 0 Solving -9 + -12b + 4b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -3b + b2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -3b + 2.25 + b2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -3b + b2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -3b + b2 = 0 + 2.25 -3b + b2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -3b + b2 = 2.25 The b term is -3b. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3b + 2.25 + b2 = 2.25 + 2.25 Reorder the terms: 2.25 + -3b + b2 = 2.25 + 2.25 Combine like terms: 2.25 + 2.25 = 4.5 2.25 + -3b + b2 = 4.5 Factor a perfect square on the left side: (b + -1.5)(b + -1.5) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (b + -1.5) equal to 2.121320344 and -2.121320344.Subproblem 1
b + -1.5 = 2.121320344 Simplifying b + -1.5 = 2.121320344 Reorder the terms: -1.5 + b = 2.121320344 Solving -1.5 + b = 2.121320344 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + b = 2.121320344 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = 2.121320344 + 1.5 b = 2.121320344 + 1.5 Combine like terms: 2.121320344 + 1.5 = 3.621320344 b = 3.621320344 Simplifying b = 3.621320344Subproblem 2
b + -1.5 = -2.121320344 Simplifying b + -1.5 = -2.121320344 Reorder the terms: -1.5 + b = -2.121320344 Solving -1.5 + b = -2.121320344 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + b = -2.121320344 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + b = -2.121320344 + 1.5 b = -2.121320344 + 1.5 Combine like terms: -2.121320344 + 1.5 = -0.621320344 b = -0.621320344 Simplifying b = -0.621320344Solution
The solution to the problem is based on the solutions from the subproblems. b = {3.621320344, -0.621320344}
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