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Simplifying 7x2 + 23x + -6000 = 0 Reorder the terms: -6000 + 23x + 7x2 = 0 Solving -6000 + 23x + 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'. -857.1428571 + 3.285714286x + x2 = 0 Move the constant term to the right: Add '857.1428571' to each side of the equation. -857.1428571 + 3.285714286x + 857.1428571 + x2 = 0 + 857.1428571 Reorder the terms: -857.1428571 + 857.1428571 + 3.285714286x + x2 = 0 + 857.1428571 Combine like terms: -857.1428571 + 857.1428571 = 0.0000000 0.0000000 + 3.285714286x + x2 = 0 + 857.1428571 3.285714286x + x2 = 0 + 857.1428571 Combine like terms: 0 + 857.1428571 = 857.1428571 3.285714286x + x2 = 857.1428571 The x term is 3.285714286x. Take half its coefficient (1.642857143). Square it (2.698979592) and add it to both sides. Add '2.698979592' to each side of the equation. 3.285714286x + 2.698979592 + x2 = 857.1428571 + 2.698979592 Reorder the terms: 2.698979592 + 3.285714286x + x2 = 857.1428571 + 2.698979592 Combine like terms: 857.1428571 + 2.698979592 = 859.841836692 2.698979592 + 3.285714286x + x2 = 859.841836692 Factor a perfect square on the left side: (x + 1.642857143)(x + 1.642857143) = 859.841836692 Calculate the square root of the right side: 29.323059811 Break this problem into two subproblems by setting (x + 1.642857143) equal to 29.323059811 and -29.323059811.Subproblem 1
x + 1.642857143 = 29.323059811 Simplifying x + 1.642857143 = 29.323059811 Reorder the terms: 1.642857143 + x = 29.323059811 Solving 1.642857143 + x = 29.323059811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.642857143' to each side of the equation. 1.642857143 + -1.642857143 + x = 29.323059811 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x = 29.323059811 + -1.642857143 x = 29.323059811 + -1.642857143 Combine like terms: 29.323059811 + -1.642857143 = 27.680202668 x = 27.680202668 Simplifying x = 27.680202668Subproblem 2
x + 1.642857143 = -29.323059811 Simplifying x + 1.642857143 = -29.323059811 Reorder the terms: 1.642857143 + x = -29.323059811 Solving 1.642857143 + x = -29.323059811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.642857143' to each side of the equation. 1.642857143 + -1.642857143 + x = -29.323059811 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + x = -29.323059811 + -1.642857143 x = -29.323059811 + -1.642857143 Combine like terms: -29.323059811 + -1.642857143 = -30.965916954 x = -30.965916954 Simplifying x = -30.965916954Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.680202668, -30.965916954}
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