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Simplifying 7x2 + -16x + -11 = 0 Reorder the terms: -11 + -16x + 7x2 = 0 Solving -11 + -16x + 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'. -1.571428571 + -2.285714286x + x2 = 0 Move the constant term to the right: Add '1.571428571' to each side of the equation. -1.571428571 + -2.285714286x + 1.571428571 + x2 = 0 + 1.571428571 Reorder the terms: -1.571428571 + 1.571428571 + -2.285714286x + x2 = 0 + 1.571428571 Combine like terms: -1.571428571 + 1.571428571 = 0.000000000 0.000000000 + -2.285714286x + x2 = 0 + 1.571428571 -2.285714286x + x2 = 0 + 1.571428571 Combine like terms: 0 + 1.571428571 = 1.571428571 -2.285714286x + x2 = 1.571428571 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 = 1.571428571 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286x + x2 = 1.571428571 + 1.306122449 Combine like terms: 1.571428571 + 1.306122449 = 2.87755102 1.306122449 + -2.285714286x + x2 = 2.87755102 Factor a perfect square on the left side: (x + -1.142857143)(x + -1.142857143) = 2.87755102 Calculate the square root of the right side: 1.696334584 Break this problem into two subproblems by setting (x + -1.142857143) equal to 1.696334584 and -1.696334584.Subproblem 1
x + -1.142857143 = 1.696334584 Simplifying x + -1.142857143 = 1.696334584 Reorder the terms: -1.142857143 + x = 1.696334584 Solving -1.142857143 + x = 1.696334584 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 = 1.696334584 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = 1.696334584 + 1.142857143 x = 1.696334584 + 1.142857143 Combine like terms: 1.696334584 + 1.142857143 = 2.839191727 x = 2.839191727 Simplifying x = 2.839191727Subproblem 2
x + -1.142857143 = -1.696334584 Simplifying x + -1.142857143 = -1.696334584 Reorder the terms: -1.142857143 + x = -1.696334584 Solving -1.142857143 + x = -1.696334584 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 = -1.696334584 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + x = -1.696334584 + 1.142857143 x = -1.696334584 + 1.142857143 Combine like terms: -1.696334584 + 1.142857143 = -0.553477441 x = -0.553477441 Simplifying x = -0.553477441Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.839191727, -0.553477441}
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