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Simplifying 4b2 + 20b + 18 = 3 Reorder the terms: 18 + 20b + 4b2 = 3 Solving 18 + 20b + 4b2 = 3 Solving for variable 'b'. Reorder the terms: 18 + -3 + 20b + 4b2 = 3 + -3 Combine like terms: 18 + -3 = 15 15 + 20b + 4b2 = 3 + -3 Combine like terms: 3 + -3 = 0 15 + 20b + 4b2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + 5b + b2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 5b + -3.75 + b2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 5b + b2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 5b + b2 = 0 + -3.75 5b + b2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 5b + b2 = -3.75 The b term is 5b. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5b + 6.25 + b2 = -3.75 + 6.25 Reorder the terms: 6.25 + 5b + b2 = -3.75 + 6.25 Combine like terms: -3.75 + 6.25 = 2.5 6.25 + 5b + b2 = 2.5 Factor a perfect square on the left side: (b + 2.5)(b + 2.5) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (b + 2.5) equal to 1.58113883 and -1.58113883.Subproblem 1
b + 2.5 = 1.58113883 Simplifying b + 2.5 = 1.58113883 Reorder the terms: 2.5 + b = 1.58113883 Solving 2.5 + b = 1.58113883 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + b = 1.58113883 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = 1.58113883 + -2.5 b = 1.58113883 + -2.5 Combine like terms: 1.58113883 + -2.5 = -0.91886117 b = -0.91886117 Simplifying b = -0.91886117Subproblem 2
b + 2.5 = -1.58113883 Simplifying b + 2.5 = -1.58113883 Reorder the terms: 2.5 + b = -1.58113883 Solving 2.5 + b = -1.58113883 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + b = -1.58113883 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + b = -1.58113883 + -2.5 b = -1.58113883 + -2.5 Combine like terms: -1.58113883 + -2.5 = -4.08113883 b = -4.08113883 Simplifying b = -4.08113883Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.91886117, -4.08113883}
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