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Simplifying -7x(x + -5) + x = -7(-2 + -1x) Reorder the terms: -7x(-5 + x) + x = -7(-2 + -1x) (-5 * -7x + x * -7x) + x = -7(-2 + -1x) (35x + -7x2) + x = -7(-2 + -1x) Reorder the terms: 35x + x + -7x2 = -7(-2 + -1x) Combine like terms: 35x + x = 36x 36x + -7x2 = -7(-2 + -1x) 36x + -7x2 = (-2 * -7 + -1x * -7) 36x + -7x2 = (14 + 7x) Solving 36x + -7x2 = 14 + 7x Solving for variable 'x'. Reorder the terms: -14 + 36x + -7x + -7x2 = 14 + 7x + -14 + -7x Combine like terms: 36x + -7x = 29x -14 + 29x + -7x2 = 14 + 7x + -14 + -7x Reorder the terms: -14 + 29x + -7x2 = 14 + -14 + 7x + -7x Combine like terms: 14 + -14 = 0 -14 + 29x + -7x2 = 0 + 7x + -7x -14 + 29x + -7x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -14 + 29x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 2 + -4.142857143x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -4.142857143x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -4.142857143x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4.142857143x + x2 = 0 + -2 -4.142857143x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4.142857143x + x2 = -2 The x term is -4.142857143x. Take half its coefficient (-2.071428572). Square it (4.290816329) and add it to both sides. Add '4.290816329' to each side of the equation. -4.142857143x + 4.290816329 + x2 = -2 + 4.290816329 Reorder the terms: 4.290816329 + -4.142857143x + x2 = -2 + 4.290816329 Combine like terms: -2 + 4.290816329 = 2.290816329 4.290816329 + -4.142857143x + x2 = 2.290816329 Factor a perfect square on the left side: (x + -2.071428572)(x + -2.071428572) = 2.290816329 Calculate the square root of the right side: 1.513544294 Break this problem into two subproblems by setting (x + -2.071428572) equal to 1.513544294 and -1.513544294.Subproblem 1
x + -2.071428572 = 1.513544294 Simplifying x + -2.071428572 = 1.513544294 Reorder the terms: -2.071428572 + x = 1.513544294 Solving -2.071428572 + x = 1.513544294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.071428572' to each side of the equation. -2.071428572 + 2.071428572 + x = 1.513544294 + 2.071428572 Combine like terms: -2.071428572 + 2.071428572 = 0.000000000 0.000000000 + x = 1.513544294 + 2.071428572 x = 1.513544294 + 2.071428572 Combine like terms: 1.513544294 + 2.071428572 = 3.584972866 x = 3.584972866 Simplifying x = 3.584972866Subproblem 2
x + -2.071428572 = -1.513544294 Simplifying x + -2.071428572 = -1.513544294 Reorder the terms: -2.071428572 + x = -1.513544294 Solving -2.071428572 + x = -1.513544294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.071428572' to each side of the equation. -2.071428572 + 2.071428572 + x = -1.513544294 + 2.071428572 Combine like terms: -2.071428572 + 2.071428572 = 0.000000000 0.000000000 + x = -1.513544294 + 2.071428572 x = -1.513544294 + 2.071428572 Combine like terms: -1.513544294 + 2.071428572 = 0.557884278 x = 0.557884278 Simplifying x = 0.557884278Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.584972866, 0.557884278}
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