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Simplifying 7x2 + 22x + -6 = 0 Reorder the terms: -6 + 22x + 7x2 = 0 Solving -6 + 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'. -0.8571428571 + 3.142857143x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 3.142857143x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 3.142857143x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 3.142857143x + x2 = 0 + 0.8571428571 3.142857143x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 3.142857143x + x2 = 0.8571428571 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 = 0.8571428571 + 2.469387757 Reorder the terms: 2.469387757 + 3.142857143x + x2 = 0.8571428571 + 2.469387757 Combine like terms: 0.8571428571 + 2.469387757 = 3.3265306141 2.469387757 + 3.142857143x + x2 = 3.3265306141 Factor a perfect square on the left side: (x + 1.571428572)(x + 1.571428572) = 3.3265306141 Calculate the square root of the right side: 1.823877905 Break this problem into two subproblems by setting (x + 1.571428572) equal to 1.823877905 and -1.823877905.Subproblem 1
x + 1.571428572 = 1.823877905 Simplifying x + 1.571428572 = 1.823877905 Reorder the terms: 1.571428572 + x = 1.823877905 Solving 1.571428572 + x = 1.823877905 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 = 1.823877905 + -1.571428572 Combine like terms: 1.571428572 + -1.571428572 = 0.000000000 0.000000000 + x = 1.823877905 + -1.571428572 x = 1.823877905 + -1.571428572 Combine like terms: 1.823877905 + -1.571428572 = 0.252449333 x = 0.252449333 Simplifying x = 0.252449333Subproblem 2
x + 1.571428572 = -1.823877905 Simplifying x + 1.571428572 = -1.823877905 Reorder the terms: 1.571428572 + x = -1.823877905 Solving 1.571428572 + x = -1.823877905 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 = -1.823877905 + -1.571428572 Combine like terms: 1.571428572 + -1.571428572 = 0.000000000 0.000000000 + x = -1.823877905 + -1.571428572 x = -1.823877905 + -1.571428572 Combine like terms: -1.823877905 + -1.571428572 = -3.395306477 x = -3.395306477 Simplifying x = -3.395306477Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.252449333, -3.395306477}
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