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Simplifying 7x2 + 22x + -41 = 0 Reorder the terms: -41 + 22x + 7x2 = 0 Solving -41 + 22x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.857142857 + 3.142857143x + x2 = 0 Move the constant term to the right: Add '5.857142857' to each side of the equation. -5.857142857 + 3.142857143x + 5.857142857 + x2 = 0 + 5.857142857 Reorder the terms: -5.857142857 + 5.857142857 + 3.142857143x + x2 = 0 + 5.857142857 Combine like terms: -5.857142857 + 5.857142857 = 0.000000000 0.000000000 + 3.142857143x + x2 = 0 + 5.857142857 3.142857143x + x2 = 0 + 5.857142857 Combine like terms: 0 + 5.857142857 = 5.857142857 3.142857143x + x2 = 5.857142857 The x term is 3.142857143x. Take half its coefficient (1.571428572). Square it (2.469387757) and add it to both sides. Add '2.469387757' to each side of the equation. 3.142857143x + 2.469387757 + x2 = 5.857142857 + 2.469387757 Reorder the terms: 2.469387757 + 3.142857143x + x2 = 5.857142857 + 2.469387757 Combine like terms: 5.857142857 + 2.469387757 = 8.326530614 2.469387757 + 3.142857143x + x2 = 8.326530614 Factor a perfect square on the left side: (x + 1.571428572)(x + 1.571428572) = 8.326530614 Calculate the square root of the right side: 2.88557284 Break this problem into two subproblems by setting (x + 1.571428572) equal to 2.88557284 and -2.88557284.Subproblem 1
x + 1.571428572 = 2.88557284 Simplifying x + 1.571428572 = 2.88557284 Reorder the terms: 1.571428572 + x = 2.88557284 Solving 1.571428572 + x = 2.88557284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.571428572' to each side of the equation. 1.571428572 + -1.571428572 + x = 2.88557284 + -1.571428572 Combine like terms: 1.571428572 + -1.571428572 = 0.000000000 0.000000000 + x = 2.88557284 + -1.571428572 x = 2.88557284 + -1.571428572 Combine like terms: 2.88557284 + -1.571428572 = 1.314144268 x = 1.314144268 Simplifying x = 1.314144268Subproblem 2
x + 1.571428572 = -2.88557284 Simplifying x + 1.571428572 = -2.88557284 Reorder the terms: 1.571428572 + x = -2.88557284 Solving 1.571428572 + x = -2.88557284 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.571428572' to each side of the equation. 1.571428572 + -1.571428572 + x = -2.88557284 + -1.571428572 Combine like terms: 1.571428572 + -1.571428572 = 0.000000000 0.000000000 + x = -2.88557284 + -1.571428572 x = -2.88557284 + -1.571428572 Combine like terms: -2.88557284 + -1.571428572 = -4.457001412 x = -4.457001412 Simplifying x = -4.457001412Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.314144268, -4.457001412}
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