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Simplifying 4b2 + -24b + -11 = 0 Reorder the terms: -11 + -24b + 4b2 = 0 Solving -11 + -24b + 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'. -2.75 + -6b + b2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -6b + 2.75 + b2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -6b + b2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -6b + b2 = 0 + 2.75 -6b + b2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -6b + b2 = 2.75 The b term is -6b. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6b + 9 + b2 = 2.75 + 9 Reorder the terms: 9 + -6b + b2 = 2.75 + 9 Combine like terms: 2.75 + 9 = 11.75 9 + -6b + b2 = 11.75 Factor a perfect square on the left side: (b + -3)(b + -3) = 11.75 Calculate the square root of the right side: 3.4278273 Break this problem into two subproblems by setting (b + -3) equal to 3.4278273 and -3.4278273.Subproblem 1
b + -3 = 3.4278273 Simplifying b + -3 = 3.4278273 Reorder the terms: -3 + b = 3.4278273 Solving -3 + b = 3.4278273 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + b = 3.4278273 + 3 Combine like terms: -3 + 3 = 0 0 + b = 3.4278273 + 3 b = 3.4278273 + 3 Combine like terms: 3.4278273 + 3 = 6.4278273 b = 6.4278273 Simplifying b = 6.4278273Subproblem 2
b + -3 = -3.4278273 Simplifying b + -3 = -3.4278273 Reorder the terms: -3 + b = -3.4278273 Solving -3 + b = -3.4278273 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + b = -3.4278273 + 3 Combine like terms: -3 + 3 = 0 0 + b = -3.4278273 + 3 b = -3.4278273 + 3 Combine like terms: -3.4278273 + 3 = -0.4278273 b = -0.4278273 Simplifying b = -0.4278273Solution
The solution to the problem is based on the solutions from the subproblems. b = {6.4278273, -0.4278273}
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