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Simplifying 14 = 196 + 28b + -1b * b Multiply b * b 14 = 196 + 28b + -1b2 Solving 14 = 196 + 28b + -1b2 Solving for variable 'b'. Combine like terms: 14 + -196 = -182 -182 + -28b + b2 = 196 + 28b + -1b2 + -196 + -28b + b2 Reorder the terms: -182 + -28b + b2 = 196 + -196 + 28b + -28b + -1b2 + b2 Combine like terms: 196 + -196 = 0 -182 + -28b + b2 = 0 + 28b + -28b + -1b2 + b2 -182 + -28b + b2 = 28b + -28b + -1b2 + b2 Combine like terms: 28b + -28b = 0 -182 + -28b + b2 = 0 + -1b2 + b2 -182 + -28b + b2 = -1b2 + b2 Combine like terms: -1b2 + b2 = 0 -182 + -28b + b2 = 0 Begin completing the square. Move the constant term to the right: Add '182' to each side of the equation. -182 + -28b + 182 + b2 = 0 + 182 Reorder the terms: -182 + 182 + -28b + b2 = 0 + 182 Combine like terms: -182 + 182 = 0 0 + -28b + b2 = 0 + 182 -28b + b2 = 0 + 182 Combine like terms: 0 + 182 = 182 -28b + b2 = 182 The b term is -28b. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28b + 196 + b2 = 182 + 196 Reorder the terms: 196 + -28b + b2 = 182 + 196 Combine like terms: 182 + 196 = 378 196 + -28b + b2 = 378 Factor a perfect square on the left side: (b + -14)(b + -14) = 378 Calculate the square root of the right side: 19.442222095 Break this problem into two subproblems by setting (b + -14) equal to 19.442222095 and -19.442222095.Subproblem 1
b + -14 = 19.442222095 Simplifying b + -14 = 19.442222095 Reorder the terms: -14 + b = 19.442222095 Solving -14 + b = 19.442222095 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + b = 19.442222095 + 14 Combine like terms: -14 + 14 = 0 0 + b = 19.442222095 + 14 b = 19.442222095 + 14 Combine like terms: 19.442222095 + 14 = 33.442222095 b = 33.442222095 Simplifying b = 33.442222095Subproblem 2
b + -14 = -19.442222095 Simplifying b + -14 = -19.442222095 Reorder the terms: -14 + b = -19.442222095 Solving -14 + b = -19.442222095 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + b = -19.442222095 + 14 Combine like terms: -14 + 14 = 0 0 + b = -19.442222095 + 14 b = -19.442222095 + 14 Combine like terms: -19.442222095 + 14 = -5.442222095 b = -5.442222095 Simplifying b = -5.442222095Solution
The solution to the problem is based on the solutions from the subproblems. b = {33.442222095, -5.442222095}
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