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Simplifying x2 + 169x + 26 = 19 Reorder the terms: 26 + 169x + x2 = 19 Solving 26 + 169x + x2 = 19 Solving for variable 'x'. Reorder the terms: 26 + -19 + 169x + x2 = 19 + -19 Combine like terms: 26 + -19 = 7 7 + 169x + x2 = 19 + -19 Combine like terms: 19 + -19 = 0 7 + 169x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 169x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 169x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 169x + x2 = 0 + -7 169x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 169x + x2 = -7 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 = -7 + 7140.25 Reorder the terms: 7140.25 + 169x + x2 = -7 + 7140.25 Combine like terms: -7 + 7140.25 = 7133.25 7140.25 + 169x + x2 = 7133.25 Factor a perfect square on the left side: (x + 84.5)(x + 84.5) = 7133.25 Calculate the square root of the right side: 84.458569725 Break this problem into two subproblems by setting (x + 84.5) equal to 84.458569725 and -84.458569725.Subproblem 1
x + 84.5 = 84.458569725 Simplifying x + 84.5 = 84.458569725 Reorder the terms: 84.5 + x = 84.458569725 Solving 84.5 + x = 84.458569725 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 = 84.458569725 + -84.5 Combine like terms: 84.5 + -84.5 = 0.0 0.0 + x = 84.458569725 + -84.5 x = 84.458569725 + -84.5 Combine like terms: 84.458569725 + -84.5 = -0.041430275 x = -0.041430275 Simplifying x = -0.041430275Subproblem 2
x + 84.5 = -84.458569725 Simplifying x + 84.5 = -84.458569725 Reorder the terms: 84.5 + x = -84.458569725 Solving 84.5 + x = -84.458569725 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 = -84.458569725 + -84.5 Combine like terms: 84.5 + -84.5 = 0.0 0.0 + x = -84.458569725 + -84.5 x = -84.458569725 + -84.5 Combine like terms: -84.458569725 + -84.5 = -168.958569725 x = -168.958569725 Simplifying x = -168.958569725Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.041430275, -168.958569725}
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