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Simplifying (7x + -5)(7x + -5) + 44 = 180 Reorder the terms: (-5 + 7x)(7x + -5) + 44 = 180 Reorder the terms: (-5 + 7x)(-5 + 7x) + 44 = 180 Multiply (-5 + 7x) * (-5 + 7x) (-5(-5 + 7x) + 7x * (-5 + 7x)) + 44 = 180 ((-5 * -5 + 7x * -5) + 7x * (-5 + 7x)) + 44 = 180 ((25 + -35x) + 7x * (-5 + 7x)) + 44 = 180 (25 + -35x + (-5 * 7x + 7x * 7x)) + 44 = 180 (25 + -35x + (-35x + 49x2)) + 44 = 180 Combine like terms: -35x + -35x = -70x (25 + -70x + 49x2) + 44 = 180 Reorder the terms: 25 + 44 + -70x + 49x2 = 180 Combine like terms: 25 + 44 = 69 69 + -70x + 49x2 = 180 Solving 69 + -70x + 49x2 = 180 Solving for variable 'x'. Reorder the terms: 69 + -180 + -70x + 49x2 = 180 + -180 Combine like terms: 69 + -180 = -111 -111 + -70x + 49x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -111 + -70x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -2.265306122 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '2.265306122' to each side of the equation. -2.265306122 + -1.428571429x + 2.265306122 + x2 = 0 + 2.265306122 Reorder the terms: -2.265306122 + 2.265306122 + -1.428571429x + x2 = 0 + 2.265306122 Combine like terms: -2.265306122 + 2.265306122 = 0.000000000 0.000000000 + -1.428571429x + x2 = 0 + 2.265306122 -1.428571429x + x2 = 0 + 2.265306122 Combine like terms: 0 + 2.265306122 = 2.265306122 -1.428571429x + x2 = 2.265306122 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 = 2.265306122 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 2.265306122 + 0.5102040819 Combine like terms: 2.265306122 + 0.5102040819 = 2.7755102039 0.5102040819 + -1.428571429x + x2 = 2.7755102039 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 2.7755102039 Calculate the square root of the right side: 1.665986256 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 1.665986256 and -1.665986256.Subproblem 1
x + -0.7142857145 = 1.665986256 Simplifying x + -0.7142857145 = 1.665986256 Reorder the terms: -0.7142857145 + x = 1.665986256 Solving -0.7142857145 + x = 1.665986256 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 = 1.665986256 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 1.665986256 + 0.7142857145 x = 1.665986256 + 0.7142857145 Combine like terms: 1.665986256 + 0.7142857145 = 2.3802719705 x = 2.3802719705 Simplifying x = 2.3802719705Subproblem 2
x + -0.7142857145 = -1.665986256 Simplifying x + -0.7142857145 = -1.665986256 Reorder the terms: -0.7142857145 + x = -1.665986256 Solving -0.7142857145 + x = -1.665986256 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 = -1.665986256 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -1.665986256 + 0.7142857145 x = -1.665986256 + 0.7142857145 Combine like terms: -1.665986256 + 0.7142857145 = -0.9517005415 x = -0.9517005415 Simplifying x = -0.9517005415Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3802719705, -0.9517005415}
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