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Simplifying x2 = 169x + -5 Reorder the terms: x2 = -5 + 169x Solving x2 = -5 + 169x Solving for variable 'x'. Reorder the terms: 5 + -169x + x2 = -5 + 169x + 5 + -169x Reorder the terms: 5 + -169x + x2 = -5 + 5 + 169x + -169x Combine like terms: -5 + 5 = 0 5 + -169x + x2 = 0 + 169x + -169x 5 + -169x + x2 = 169x + -169x Combine like terms: 169x + -169x = 0 5 + -169x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -169x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -169x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -169x + x2 = 0 + -5 -169x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -169x + x2 = -5 The x term is -169x. Take half its coefficient (-84.5). Square it (7140.25) and add it to both sides. Add '7140.25' to each side of the equation. -169x + 7140.25 + x2 = -5 + 7140.25 Reorder the terms: 7140.25 + -169x + x2 = -5 + 7140.25 Combine like terms: -5 + 7140.25 = 7135.25 7140.25 + -169x + x2 = 7135.25 Factor a perfect square on the left side: (x + -84.5)(x + -84.5) = 7135.25 Calculate the square root of the right side: 84.47040902 Break this problem into two subproblems by setting (x + -84.5) equal to 84.47040902 and -84.47040902.Subproblem 1
x + -84.5 = 84.47040902 Simplifying x + -84.5 = 84.47040902 Reorder the terms: -84.5 + x = 84.47040902 Solving -84.5 + x = 84.47040902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '84.5' to each side of the equation. -84.5 + 84.5 + x = 84.47040902 + 84.5 Combine like terms: -84.5 + 84.5 = 0.0 0.0 + x = 84.47040902 + 84.5 x = 84.47040902 + 84.5 Combine like terms: 84.47040902 + 84.5 = 168.97040902 x = 168.97040902 Simplifying x = 168.97040902Subproblem 2
x + -84.5 = -84.47040902 Simplifying x + -84.5 = -84.47040902 Reorder the terms: -84.5 + x = -84.47040902 Solving -84.5 + x = -84.47040902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '84.5' to each side of the equation. -84.5 + 84.5 + x = -84.47040902 + 84.5 Combine like terms: -84.5 + 84.5 = 0.0 0.0 + x = -84.47040902 + 84.5 x = -84.47040902 + 84.5 Combine like terms: -84.47040902 + 84.5 = 0.02959098 x = 0.02959098 Simplifying x = 0.02959098Solution
The solution to the problem is based on the solutions from the subproblems. x = {168.97040902, 0.02959098}
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