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Simplifying 7x2 = 16x + 38 Reorder the terms: 7x2 = 38 + 16x Solving 7x2 = 38 + 16x Solving for variable 'x'. Reorder the terms: -38 + -16x + 7x2 = 38 + 16x + -38 + -16x Reorder the terms: -38 + -16x + 7x2 = 38 + -38 + 16x + -16x Combine like terms: 38 + -38 = 0 -38 + -16x + 7x2 = 0 + 16x + -16x -38 + -16x + 7x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -38 + -16x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.428571429 + -2.285714286x + x2 = 0 Move the constant term to the right: Add '5.428571429' to each side of the equation. -5.428571429 + -2.285714286x + 5.428571429 + x2 = 0 + 5.428571429 Reorder the terms: -5.428571429 + 5.428571429 + -2.285714286x + x2 = 0 + 5.428571429 Combine like terms: -5.428571429 + 5.428571429 = 0.000000000 0.000000000 + -2.285714286x + x2 = 0 + 5.428571429 -2.285714286x + x2 = 0 + 5.428571429 Combine like terms: 0 + 5.428571429 = 5.428571429 -2.285714286x + x2 = 5.428571429 The x term is -2.285714286x. Take half its coefficient (-1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. -2.285714286x + 1.306122449 + x2 = 5.428571429 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286x + x2 = 5.428571429 + 1.306122449 Combine like terms: 5.428571429 + 1.306122449 = 6.734693878 1.306122449 + -2.285714286x + x2 = 6.734693878 Factor a perfect square on the left side: (x + -1.142857143)(x + -1.142857143) = 6.734693878 Calculate the square root of the right side: 2.595128875 Break this problem into two subproblems by setting (x + -1.142857143) equal to 2.595128875 and -2.595128875.Subproblem 1
x + -1.142857143 = 2.595128875 Simplifying x + -1.142857143 = 2.595128875 Reorder the terms: -1.142857143 + x = 2.595128875 Solving -1.142857143 + x = 2.595128875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x = 2.595128875 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = 2.595128875 + 1.142857143 x = 2.595128875 + 1.142857143 Combine like terms: 2.595128875 + 1.142857143 = 3.737986018 x = 3.737986018 Simplifying x = 3.737986018Subproblem 2
x + -1.142857143 = -2.595128875 Simplifying x + -1.142857143 = -2.595128875 Reorder the terms: -1.142857143 + x = -2.595128875 Solving -1.142857143 + x = -2.595128875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + x = -2.595128875 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = -2.595128875 + 1.142857143 x = -2.595128875 + 1.142857143 Combine like terms: -2.595128875 + 1.142857143 = -1.452271732 x = -1.452271732 Simplifying x = -1.452271732Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.737986018, -1.452271732}
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