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Simplifying 4b2 + -22b + 10 = 8 Reorder the terms: 10 + -22b + 4b2 = 8 Solving 10 + -22b + 4b2 = 8 Solving for variable 'b'. Reorder the terms: 10 + -8 + -22b + 4b2 = 8 + -8 Combine like terms: 10 + -8 = 2 2 + -22b + 4b2 = 8 + -8 Combine like terms: 8 + -8 = 0 2 + -22b + 4b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -11b + 2b2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -11b + 2b2)' equal to zero and attempt to solve: Simplifying 1 + -11b + 2b2 = 0 Solving 1 + -11b + 2b2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -5.5b + b2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -5.5b + -0.5 + b2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -5.5b + b2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -5.5b + b2 = 0 + -0.5 -5.5b + b2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -5.5b + b2 = -0.5 The b term is -5.5b. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5b + 7.5625 + b2 = -0.5 + 7.5625 Reorder the terms: 7.5625 + -5.5b + b2 = -0.5 + 7.5625 Combine like terms: -0.5 + 7.5625 = 7.0625 7.5625 + -5.5b + b2 = 7.0625 Factor a perfect square on the left side: (b + -2.75)(b + -2.75) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (b + -2.75) equal to 2.657536453 and -2.657536453.Subproblem 1
b + -2.75 = 2.657536453 Simplifying b + -2.75 = 2.657536453 Reorder the terms: -2.75 + b = 2.657536453 Solving -2.75 + b = 2.657536453 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + b = 2.657536453 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + b = 2.657536453 + 2.75 b = 2.657536453 + 2.75 Combine like terms: 2.657536453 + 2.75 = 5.407536453 b = 5.407536453 Simplifying b = 5.407536453Subproblem 2
b + -2.75 = -2.657536453 Simplifying b + -2.75 = -2.657536453 Reorder the terms: -2.75 + b = -2.657536453 Solving -2.75 + b = -2.657536453 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + b = -2.657536453 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + b = -2.657536453 + 2.75 b = -2.657536453 + 2.75 Combine like terms: -2.657536453 + 2.75 = 0.092463547 b = 0.092463547 Simplifying b = 0.092463547Solution
The solution to the problem is based on the solutions from the subproblems. b = {5.407536453, 0.092463547}Solution
b = {5.407536453, 0.092463547}
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