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Simplifying -1x + -1x(13 + 4x) = -3(5 + -9x) + 2 -1x + (13 * -1x + 4x * -1x) = -3(5 + -9x) + 2 -1x + (-13x + -4x2) = -3(5 + -9x) + 2 Combine like terms: -1x + -13x = -14x -14x + -4x2 = -3(5 + -9x) + 2 -14x + -4x2 = (5 * -3 + -9x * -3) + 2 -14x + -4x2 = (-15 + 27x) + 2 Reorder the terms: -14x + -4x2 = -15 + 2 + 27x Combine like terms: -15 + 2 = -13 -14x + -4x2 = -13 + 27x Solving -14x + -4x2 = -13 + 27x Solving for variable 'x'. Reorder the terms: 13 + -14x + -27x + -4x2 = -13 + 27x + 13 + -27x Combine like terms: -14x + -27x = -41x 13 + -41x + -4x2 = -13 + 27x + 13 + -27x Reorder the terms: 13 + -41x + -4x2 = -13 + 13 + 27x + -27x Combine like terms: -13 + 13 = 0 13 + -41x + -4x2 = 0 + 27x + -27x 13 + -41x + -4x2 = 27x + -27x Combine like terms: 27x + -27x = 0 13 + -41x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3.25 + 10.25x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 10.25x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 10.25x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 10.25x + x2 = 0 + 3.25 10.25x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 10.25x + x2 = 3.25 The x term is 10.25x. Take half its coefficient (5.125). Square it (26.265625) and add it to both sides. Add '26.265625' to each side of the equation. 10.25x + 26.265625 + x2 = 3.25 + 26.265625 Reorder the terms: 26.265625 + 10.25x + x2 = 3.25 + 26.265625 Combine like terms: 3.25 + 26.265625 = 29.515625 26.265625 + 10.25x + x2 = 29.515625 Factor a perfect square on the left side: (x + 5.125)(x + 5.125) = 29.515625 Calculate the square root of the right side: 5.432828453 Break this problem into two subproblems by setting (x + 5.125) equal to 5.432828453 and -5.432828453.Subproblem 1
x + 5.125 = 5.432828453 Simplifying x + 5.125 = 5.432828453 Reorder the terms: 5.125 + x = 5.432828453 Solving 5.125 + x = 5.432828453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.125' to each side of the equation. 5.125 + -5.125 + x = 5.432828453 + -5.125 Combine like terms: 5.125 + -5.125 = 0.000 0.000 + x = 5.432828453 + -5.125 x = 5.432828453 + -5.125 Combine like terms: 5.432828453 + -5.125 = 0.307828453 x = 0.307828453 Simplifying x = 0.307828453Subproblem 2
x + 5.125 = -5.432828453 Simplifying x + 5.125 = -5.432828453 Reorder the terms: 5.125 + x = -5.432828453 Solving 5.125 + x = -5.432828453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.125' to each side of the equation. 5.125 + -5.125 + x = -5.432828453 + -5.125 Combine like terms: 5.125 + -5.125 = 0.000 0.000 + x = -5.432828453 + -5.125 x = -5.432828453 + -5.125 Combine like terms: -5.432828453 + -5.125 = -10.557828453 x = -10.557828453 Simplifying x = -10.557828453Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.307828453, -10.557828453}
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