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Simplifying (7x + -5)(7x + -5) = 14 Reorder the terms: (-5 + 7x)(7x + -5) = 14 Reorder the terms: (-5 + 7x)(-5 + 7x) = 14 Multiply (-5 + 7x) * (-5 + 7x) (-5(-5 + 7x) + 7x * (-5 + 7x)) = 14 ((-5 * -5 + 7x * -5) + 7x * (-5 + 7x)) = 14 ((25 + -35x) + 7x * (-5 + 7x)) = 14 (25 + -35x + (-5 * 7x + 7x * 7x)) = 14 (25 + -35x + (-35x + 49x2)) = 14 Combine like terms: -35x + -35x = -70x (25 + -70x + 49x2) = 14 Solving 25 + -70x + 49x2 = 14 Solving for variable 'x'. Reorder the terms: 25 + -14 + -70x + 49x2 = 14 + -14 Combine like terms: 25 + -14 = 11 11 + -70x + 49x2 = 14 + -14 Combine like terms: 14 + -14 = 0 11 + -70x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.2244897959 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '-0.2244897959' to each side of the equation. 0.2244897959 + -1.428571429x + -0.2244897959 + x2 = 0 + -0.2244897959 Reorder the terms: 0.2244897959 + -0.2244897959 + -1.428571429x + x2 = 0 + -0.2244897959 Combine like terms: 0.2244897959 + -0.2244897959 = 0.0000000000 0.0000000000 + -1.428571429x + x2 = 0 + -0.2244897959 -1.428571429x + x2 = 0 + -0.2244897959 Combine like terms: 0 + -0.2244897959 = -0.2244897959 -1.428571429x + x2 = -0.2244897959 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 = -0.2244897959 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = -0.2244897959 + 0.5102040819 Combine like terms: -0.2244897959 + 0.5102040819 = 0.285714286 0.5102040819 + -1.428571429x + x2 = 0.285714286 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 0.285714286 Calculate the square root of the right side: 0.534522484 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 0.534522484 and -0.534522484.Subproblem 1
x + -0.7142857145 = 0.534522484 Simplifying x + -0.7142857145 = 0.534522484 Reorder the terms: -0.7142857145 + x = 0.534522484 Solving -0.7142857145 + x = 0.534522484 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 = 0.534522484 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 0.534522484 + 0.7142857145 x = 0.534522484 + 0.7142857145 Combine like terms: 0.534522484 + 0.7142857145 = 1.2488081985 x = 1.2488081985 Simplifying x = 1.2488081985Subproblem 2
x + -0.7142857145 = -0.534522484 Simplifying x + -0.7142857145 = -0.534522484 Reorder the terms: -0.7142857145 + x = -0.534522484 Solving -0.7142857145 + x = -0.534522484 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 = -0.534522484 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -0.534522484 + 0.7142857145 x = -0.534522484 + 0.7142857145 Combine like terms: -0.534522484 + 0.7142857145 = 0.1797632305 x = 0.1797632305 Simplifying x = 0.1797632305Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2488081985, 0.1797632305}
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