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Simplifying 9x2 + 240x + -1000 = 0 Reorder the terms: -1000 + 240x + 9x2 = 0 Solving -1000 + 240x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -111.1111111 + 26.66666667x + x2 = 0 Move the constant term to the right: Add '111.1111111' to each side of the equation. -111.1111111 + 26.66666667x + 111.1111111 + x2 = 0 + 111.1111111 Reorder the terms: -111.1111111 + 111.1111111 + 26.66666667x + x2 = 0 + 111.1111111 Combine like terms: -111.1111111 + 111.1111111 = 0.0000000 0.0000000 + 26.66666667x + x2 = 0 + 111.1111111 26.66666667x + x2 = 0 + 111.1111111 Combine like terms: 0 + 111.1111111 = 111.1111111 26.66666667x + x2 = 111.1111111 The x term is 26.66666667x. Take half its coefficient (13.33333334). Square it (177.7777780) and add it to both sides. Add '177.7777780' to each side of the equation. 26.66666667x + 177.7777780 + x2 = 111.1111111 + 177.7777780 Reorder the terms: 177.7777780 + 26.66666667x + x2 = 111.1111111 + 177.7777780 Combine like terms: 111.1111111 + 177.7777780 = 288.8888891 177.7777780 + 26.66666667x + x2 = 288.8888891 Factor a perfect square on the left side: (x + 13.33333334)(x + 13.33333334) = 288.8888891 Calculate the square root of the right side: 16.996731718 Break this problem into two subproblems by setting (x + 13.33333334) equal to 16.996731718 and -16.996731718.Subproblem 1
x + 13.33333334 = 16.996731718 Simplifying x + 13.33333334 = 16.996731718 Reorder the terms: 13.33333334 + x = 16.996731718 Solving 13.33333334 + x = 16.996731718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.33333334' to each side of the equation. 13.33333334 + -13.33333334 + x = 16.996731718 + -13.33333334 Combine like terms: 13.33333334 + -13.33333334 = 0.00000000 0.00000000 + x = 16.996731718 + -13.33333334 x = 16.996731718 + -13.33333334 Combine like terms: 16.996731718 + -13.33333334 = 3.663398378 x = 3.663398378 Simplifying x = 3.663398378Subproblem 2
x + 13.33333334 = -16.996731718 Simplifying x + 13.33333334 = -16.996731718 Reorder the terms: 13.33333334 + x = -16.996731718 Solving 13.33333334 + x = -16.996731718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.33333334' to each side of the equation. 13.33333334 + -13.33333334 + x = -16.996731718 + -13.33333334 Combine like terms: 13.33333334 + -13.33333334 = 0.00000000 0.00000000 + x = -16.996731718 + -13.33333334 x = -16.996731718 + -13.33333334 Combine like terms: -16.996731718 + -13.33333334 = -30.330065058 x = -30.330065058 Simplifying x = -30.330065058Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.663398378, -30.330065058}
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