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Simplifying 7x2 + -16x = 1 Reorder the terms: -16x + 7x2 = 1 Solving -16x + 7x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -16x + 7x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -16x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -2.285714286x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -2.285714286x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -2.285714286x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -2.285714286x + x2 = 0 + 0.1428571429 -2.285714286x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -2.285714286x + x2 = 0.1428571429 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 = 0.1428571429 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286x + x2 = 0.1428571429 + 1.306122449 Combine like terms: 0.1428571429 + 1.306122449 = 1.4489795919 1.306122449 + -2.285714286x + x2 = 1.4489795919 Factor a perfect square on the left side: (x + -1.142857143)(x + -1.142857143) = 1.4489795919 Calculate the square root of the right side: 1.203735682 Break this problem into two subproblems by setting (x + -1.142857143) equal to 1.203735682 and -1.203735682.Subproblem 1
x + -1.142857143 = 1.203735682 Simplifying x + -1.142857143 = 1.203735682 Reorder the terms: -1.142857143 + x = 1.203735682 Solving -1.142857143 + x = 1.203735682 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 = 1.203735682 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = 1.203735682 + 1.142857143 x = 1.203735682 + 1.142857143 Combine like terms: 1.203735682 + 1.142857143 = 2.346592825 x = 2.346592825 Simplifying x = 2.346592825Subproblem 2
x + -1.142857143 = -1.203735682 Simplifying x + -1.142857143 = -1.203735682 Reorder the terms: -1.142857143 + x = -1.203735682 Solving -1.142857143 + x = -1.203735682 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 = -1.203735682 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = -1.203735682 + 1.142857143 x = -1.203735682 + 1.142857143 Combine like terms: -1.203735682 + 1.142857143 = -0.060878539 x = -0.060878539 Simplifying x = -0.060878539Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.346592825, -0.060878539}
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