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Simplifying x(7x + 2) = 8 Reorder the terms: x(2 + 7x) = 8 (2 * x + 7x * x) = 8 (2x + 7x2) = 8 Solving 2x + 7x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 2x + 7x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 0.2857142857x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 0.2857142857x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 0.2857142857x + x2 = 0 + 1.142857143 0.2857142857x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 0.2857142857x + x2 = 1.142857143 The x term is 0.2857142857x. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857x + 0.02040816328 + x2 = 1.142857143 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 1.142857143 + 0.02040816328 Combine like terms: 1.142857143 + 0.02040816328 = 1.16326530628 0.02040816328 + 0.2857142857x + x2 = 1.16326530628 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 1.16326530628 Calculate the square root of the right side: 1.078547777 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 1.078547777 and -1.078547777.Subproblem 1
x + 0.1428571429 = 1.078547777 Simplifying x + 0.1428571429 = 1.078547777 Reorder the terms: 0.1428571429 + x = 1.078547777 Solving 0.1428571429 + x = 1.078547777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = 1.078547777 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 1.078547777 + -0.1428571429 x = 1.078547777 + -0.1428571429 Combine like terms: 1.078547777 + -0.1428571429 = 0.9356906341 x = 0.9356906341 Simplifying x = 0.9356906341Subproblem 2
x + 0.1428571429 = -1.078547777 Simplifying x + 0.1428571429 = -1.078547777 Reorder the terms: 0.1428571429 + x = -1.078547777 Solving 0.1428571429 + x = -1.078547777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = -1.078547777 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -1.078547777 + -0.1428571429 x = -1.078547777 + -0.1428571429 Combine like terms: -1.078547777 + -0.1428571429 = -1.2214049199 x = -1.2214049199 Simplifying x = -1.2214049199Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9356906341, -1.2214049199}
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