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Simplifying 4x2 + -52x + 169 = 8 Reorder the terms: 169 + -52x + 4x2 = 8 Solving 169 + -52x + 4x2 = 8 Solving for variable 'x'. Reorder the terms: 169 + -8 + -52x + 4x2 = 8 + -8 Combine like terms: 169 + -8 = 161 161 + -52x + 4x2 = 8 + -8 Combine like terms: 8 + -8 = 0 161 + -52x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 40.25 + -13x + x2 = 0 Move the constant term to the right: Add '-40.25' to each side of the equation. 40.25 + -13x + -40.25 + x2 = 0 + -40.25 Reorder the terms: 40.25 + -40.25 + -13x + x2 = 0 + -40.25 Combine like terms: 40.25 + -40.25 = 0.00 0.00 + -13x + x2 = 0 + -40.25 -13x + x2 = 0 + -40.25 Combine like terms: 0 + -40.25 = -40.25 -13x + x2 = -40.25 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -40.25 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -40.25 + 42.25 Combine like terms: -40.25 + 42.25 = 2 42.25 + -13x + x2 = 2 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -6.5) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -6.5 = 1.414213562 Simplifying x + -6.5 = 1.414213562 Reorder the terms: -6.5 + x = 1.414213562 Solving -6.5 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 1.414213562 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 1.414213562 + 6.5 x = 1.414213562 + 6.5 Combine like terms: 1.414213562 + 6.5 = 7.914213562 x = 7.914213562 Simplifying x = 7.914213562Subproblem 2
x + -6.5 = -1.414213562 Simplifying x + -6.5 = -1.414213562 Reorder the terms: -6.5 + x = -1.414213562 Solving -6.5 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -1.414213562 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -1.414213562 + 6.5 x = -1.414213562 + 6.5 Combine like terms: -1.414213562 + 6.5 = 5.085786438 x = 5.085786438 Simplifying x = 5.085786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.914213562, 5.085786438}
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