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Simplifying -1x(13 + 4x) = -3(5 + -9x) + 2 (13 * -1x + 4x * -1x) = -3(5 + -9x) + 2 (-13x + -4x2) = -3(5 + -9x) + 2 -13x + -4x2 = (5 * -3 + -9x * -3) + 2 -13x + -4x2 = (-15 + 27x) + 2 Reorder the terms: -13x + -4x2 = -15 + 2 + 27x Combine like terms: -15 + 2 = -13 -13x + -4x2 = -13 + 27x Solving -13x + -4x2 = -13 + 27x Solving for variable 'x'. Reorder the terms: 13 + -13x + -27x + -4x2 = -13 + 27x + 13 + -27x Combine like terms: -13x + -27x = -40x 13 + -40x + -4x2 = -13 + 27x + 13 + -27x Reorder the terms: 13 + -40x + -4x2 = -13 + 13 + 27x + -27x Combine like terms: -13 + 13 = 0 13 + -40x + -4x2 = 0 + 27x + -27x 13 + -40x + -4x2 = 27x + -27x Combine like terms: 27x + -27x = 0 13 + -40x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3.25 + 10x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 10x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 10x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 10x + x2 = 0 + 3.25 10x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 10x + x2 = 3.25 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 3.25 + 25 Reorder the terms: 25 + 10x + x2 = 3.25 + 25 Combine like terms: 3.25 + 25 = 28.25 25 + 10x + x2 = 28.25 Factor a perfect square on the left side: (x + 5)(x + 5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + 5) equal to 5.315072906 and -5.315072906.Subproblem 1
x + 5 = 5.315072906 Simplifying x + 5 = 5.315072906 Reorder the terms: 5 + x = 5.315072906 Solving 5 + x = 5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.315072906 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.315072906 + -5 x = 5.315072906 + -5 Combine like terms: 5.315072906 + -5 = 0.315072906 x = 0.315072906 Simplifying x = 0.315072906Subproblem 2
x + 5 = -5.315072906 Simplifying x + 5 = -5.315072906 Reorder the terms: 5 + x = -5.315072906 Solving 5 + x = -5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.315072906 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.315072906 + -5 x = -5.315072906 + -5 Combine like terms: -5.315072906 + -5 = -10.315072906 x = -10.315072906 Simplifying x = -10.315072906Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.315072906, -10.315072906}
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