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Simplifying (13 + -1x) * x(-8) = -19 Reorder the terms for easier multiplication: -8x(13 + -1x) = -19 (13 * -8x + -1x * -8x) = -19 (-104x + 8x2) = -19 Solving -104x + 8x2 = -19 Solving for variable 'x'. Reorder the terms: 19 + -104x + 8x2 = -19 + 19 Combine like terms: -19 + 19 = 0 19 + -104x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.375 + -13x + x2 = 0 Move the constant term to the right: Add '-2.375' to each side of the equation. 2.375 + -13x + -2.375 + x2 = 0 + -2.375 Reorder the terms: 2.375 + -2.375 + -13x + x2 = 0 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + -13x + x2 = 0 + -2.375 -13x + x2 = 0 + -2.375 Combine like terms: 0 + -2.375 = -2.375 -13x + x2 = -2.375 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 = -2.375 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -2.375 + 42.25 Combine like terms: -2.375 + 42.25 = 39.875 42.25 + -13x + x2 = 39.875 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 39.875 Calculate the square root of the right side: 6.31466547 Break this problem into two subproblems by setting (x + -6.5) equal to 6.31466547 and -6.31466547.Subproblem 1
x + -6.5 = 6.31466547 Simplifying x + -6.5 = 6.31466547 Reorder the terms: -6.5 + x = 6.31466547 Solving -6.5 + x = 6.31466547 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 = 6.31466547 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.31466547 + 6.5 x = 6.31466547 + 6.5 Combine like terms: 6.31466547 + 6.5 = 12.81466547 x = 12.81466547 Simplifying x = 12.81466547Subproblem 2
x + -6.5 = -6.31466547 Simplifying x + -6.5 = -6.31466547 Reorder the terms: -6.5 + x = -6.31466547 Solving -6.5 + x = -6.31466547 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 = -6.31466547 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.31466547 + 6.5 x = -6.31466547 + 6.5 Combine like terms: -6.31466547 + 6.5 = 0.18533453 x = 0.18533453 Simplifying x = 0.18533453Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.81466547, 0.18533453}
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