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Simplifying 10b2 + 72b + 57 = 0 Reorder the terms: 57 + 72b + 10b2 = 0 Solving 57 + 72b + 10b2 = 0 Solving for variable 'b'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 5.7 + 7.2b + b2 = 0 Move the constant term to the right: Add '-5.7' to each side of the equation. 5.7 + 7.2b + -5.7 + b2 = 0 + -5.7 Reorder the terms: 5.7 + -5.7 + 7.2b + b2 = 0 + -5.7 Combine like terms: 5.7 + -5.7 = 0.0 0.0 + 7.2b + b2 = 0 + -5.7 7.2b + b2 = 0 + -5.7 Combine like terms: 0 + -5.7 = -5.7 7.2b + b2 = -5.7 The b term is 7.2b. Take half its coefficient (3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. 7.2b + 12.96 + b2 = -5.7 + 12.96 Reorder the terms: 12.96 + 7.2b + b2 = -5.7 + 12.96 Combine like terms: -5.7 + 12.96 = 7.26 12.96 + 7.2b + b2 = 7.26 Factor a perfect square on the left side: (b + 3.6)(b + 3.6) = 7.26 Calculate the square root of the right side: 2.694438717 Break this problem into two subproblems by setting (b + 3.6) equal to 2.694438717 and -2.694438717.Subproblem 1
b + 3.6 = 2.694438717 Simplifying b + 3.6 = 2.694438717 Reorder the terms: 3.6 + b = 2.694438717 Solving 3.6 + b = 2.694438717 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + b = 2.694438717 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + b = 2.694438717 + -3.6 b = 2.694438717 + -3.6 Combine like terms: 2.694438717 + -3.6 = -0.905561283 b = -0.905561283 Simplifying b = -0.905561283Subproblem 2
b + 3.6 = -2.694438717 Simplifying b + 3.6 = -2.694438717 Reorder the terms: 3.6 + b = -2.694438717 Solving 3.6 + b = -2.694438717 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + b = -2.694438717 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + b = -2.694438717 + -3.6 b = -2.694438717 + -3.6 Combine like terms: -2.694438717 + -3.6 = -6.294438717 b = -6.294438717 Simplifying b = -6.294438717Solution
The solution to the problem is based on the solutions from the subproblems. b = {-0.905561283, -6.294438717}
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