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Simplifying (7x + -5)(7x + -5) = 26 Reorder the terms: (-5 + 7x)(7x + -5) = 26 Reorder the terms: (-5 + 7x)(-5 + 7x) = 26 Multiply (-5 + 7x) * (-5 + 7x) (-5(-5 + 7x) + 7x * (-5 + 7x)) = 26 ((-5 * -5 + 7x * -5) + 7x * (-5 + 7x)) = 26 ((25 + -35x) + 7x * (-5 + 7x)) = 26 (25 + -35x + (-5 * 7x + 7x * 7x)) = 26 (25 + -35x + (-35x + 49x2)) = 26 Combine like terms: -35x + -35x = -70x (25 + -70x + 49x2) = 26 Solving 25 + -70x + 49x2 = 26 Solving for variable 'x'. Reorder the terms: 25 + -26 + -70x + 49x2 = 26 + -26 Combine like terms: 25 + -26 = -1 -1 + -70x + 49x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -1 + -70x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.02040816327 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '0.02040816327' to each side of the equation. -0.02040816327 + -1.428571429x + 0.02040816327 + x2 = 0 + 0.02040816327 Reorder the terms: -0.02040816327 + 0.02040816327 + -1.428571429x + x2 = 0 + 0.02040816327 Combine like terms: -0.02040816327 + 0.02040816327 = 0.00000000000 0.00000000000 + -1.428571429x + x2 = 0 + 0.02040816327 -1.428571429x + x2 = 0 + 0.02040816327 Combine like terms: 0 + 0.02040816327 = 0.02040816327 -1.428571429x + x2 = 0.02040816327 The x term is -1.428571429x. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429x + 0.5102040819 + x2 = 0.02040816327 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 0.02040816327 + 0.5102040819 Combine like terms: 0.02040816327 + 0.5102040819 = 0.53061224517 0.5102040819 + -1.428571429x + x2 = 0.53061224517 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 0.53061224517 Calculate the square root of the right side: 0.728431359 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 0.728431359 and -0.728431359.Subproblem 1
x + -0.7142857145 = 0.728431359 Simplifying x + -0.7142857145 = 0.728431359 Reorder the terms: -0.7142857145 + x = 0.728431359 Solving -0.7142857145 + x = 0.728431359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 0.728431359 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 0.728431359 + 0.7142857145 x = 0.728431359 + 0.7142857145 Combine like terms: 0.728431359 + 0.7142857145 = 1.4427170735 x = 1.4427170735 Simplifying x = 1.4427170735Subproblem 2
x + -0.7142857145 = -0.728431359 Simplifying x + -0.7142857145 = -0.728431359 Reorder the terms: -0.7142857145 + x = -0.728431359 Solving -0.7142857145 + x = -0.728431359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -0.728431359 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -0.728431359 + 0.7142857145 x = -0.728431359 + 0.7142857145 Combine like terms: -0.728431359 + 0.7142857145 = -0.0141456445 x = -0.0141456445 Simplifying x = -0.0141456445Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4427170735, -0.0141456445}
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