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Simplifying -9.8x2 + 26x + 1200 = 0 Reorder the terms: 1200 + 26x + -9.8x2 = 0 Solving 1200 + 26x + -9.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9.8 the coefficient of the squared term: Divide each side by '-9.8'. -122.4489796 + -2.653061224x + x2 = 0 Move the constant term to the right: Add '122.4489796' to each side of the equation. -122.4489796 + -2.653061224x + 122.4489796 + x2 = 0 + 122.4489796 Reorder the terms: -122.4489796 + 122.4489796 + -2.653061224x + x2 = 0 + 122.4489796 Combine like terms: -122.4489796 + 122.4489796 = 0.0000000 0.0000000 + -2.653061224x + x2 = 0 + 122.4489796 -2.653061224x + x2 = 0 + 122.4489796 Combine like terms: 0 + 122.4489796 = 122.4489796 -2.653061224x + x2 = 122.4489796 The x term is -2.653061224x. Take half its coefficient (-1.326530612). Square it (1.759683465) and add it to both sides. Add '1.759683465' to each side of the equation. -2.653061224x + 1.759683465 + x2 = 122.4489796 + 1.759683465 Reorder the terms: 1.759683465 + -2.653061224x + x2 = 122.4489796 + 1.759683465 Combine like terms: 122.4489796 + 1.759683465 = 124.208663065 1.759683465 + -2.653061224x + x2 = 124.208663065 Factor a perfect square on the left side: (x + -1.326530612)(x + -1.326530612) = 124.208663065 Calculate the square root of the right side: 11.144894036 Break this problem into two subproblems by setting (x + -1.326530612) equal to 11.144894036 and -11.144894036.Subproblem 1
x + -1.326530612 = 11.144894036 Simplifying x + -1.326530612 = 11.144894036 Reorder the terms: -1.326530612 + x = 11.144894036 Solving -1.326530612 + x = 11.144894036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.326530612' to each side of the equation. -1.326530612 + 1.326530612 + x = 11.144894036 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + x = 11.144894036 + 1.326530612 x = 11.144894036 + 1.326530612 Combine like terms: 11.144894036 + 1.326530612 = 12.471424648 x = 12.471424648 Simplifying x = 12.471424648Subproblem 2
x + -1.326530612 = -11.144894036 Simplifying x + -1.326530612 = -11.144894036 Reorder the terms: -1.326530612 + x = -11.144894036 Solving -1.326530612 + x = -11.144894036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.326530612' to each side of the equation. -1.326530612 + 1.326530612 + x = -11.144894036 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + x = -11.144894036 + 1.326530612 x = -11.144894036 + 1.326530612 Combine like terms: -11.144894036 + 1.326530612 = -9.818363424 x = -9.818363424 Simplifying x = -9.818363424Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.471424648, -9.818363424}
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