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Simplifying 7x2 + 36x + 1 = 0 Reorder the terms: 1 + 36x + 7x2 = 0 Solving 1 + 36x + 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'. 0.1428571429 + 5.142857143x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 5.142857143x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 5.142857143x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 5.142857143x + x2 = 0 + -0.1428571429 5.142857143x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 5.142857143x + x2 = -0.1428571429 The x term is 5.142857143x. Take half its coefficient (2.571428572). Square it (6.612244901) and add it to both sides. Add '6.612244901' to each side of the equation. 5.142857143x + 6.612244901 + x2 = -0.1428571429 + 6.612244901 Reorder the terms: 6.612244901 + 5.142857143x + x2 = -0.1428571429 + 6.612244901 Combine like terms: -0.1428571429 + 6.612244901 = 6.4693877581 6.612244901 + 5.142857143x + x2 = 6.4693877581 Factor a perfect square on the left side: (x + 2.571428572)(x + 2.571428572) = 6.4693877581 Calculate the square root of the right side: 2.543499117 Break this problem into two subproblems by setting (x + 2.571428572) equal to 2.543499117 and -2.543499117.Subproblem 1
x + 2.571428572 = 2.543499117 Simplifying x + 2.571428572 = 2.543499117 Reorder the terms: 2.571428572 + x = 2.543499117 Solving 2.571428572 + x = 2.543499117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.571428572' to each side of the equation. 2.571428572 + -2.571428572 + x = 2.543499117 + -2.571428572 Combine like terms: 2.571428572 + -2.571428572 = 0.000000000 0.000000000 + x = 2.543499117 + -2.571428572 x = 2.543499117 + -2.571428572 Combine like terms: 2.543499117 + -2.571428572 = -0.027929455 x = -0.027929455 Simplifying x = -0.027929455Subproblem 2
x + 2.571428572 = -2.543499117 Simplifying x + 2.571428572 = -2.543499117 Reorder the terms: 2.571428572 + x = -2.543499117 Solving 2.571428572 + x = -2.543499117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.571428572' to each side of the equation. 2.571428572 + -2.571428572 + x = -2.543499117 + -2.571428572 Combine like terms: 2.571428572 + -2.571428572 = 0.000000000 0.000000000 + x = -2.543499117 + -2.571428572 x = -2.543499117 + -2.571428572 Combine like terms: -2.543499117 + -2.571428572 = -5.114927689 x = -5.114927689 Simplifying x = -5.114927689Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.027929455, -5.114927689}
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