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Simplifying x2 + 3x + -1200 = 0 Reorder the terms: -1200 + 3x + x2 = 0 Solving -1200 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1200' to each side of the equation. -1200 + 3x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + 3x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + 3x + x2 = 0 + 1200 3x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 3x + x2 = 1200 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 1200 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 1200 + 2.25 Combine like terms: 1200 + 2.25 = 1202.25 2.25 + 3x + x2 = 1202.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1202.25 Calculate the square root of the right side: 34.673476895 Break this problem into two subproblems by setting (x + 1.5) equal to 34.673476895 and -34.673476895.Subproblem 1
x + 1.5 = 34.673476895 Simplifying x + 1.5 = 34.673476895 Reorder the terms: 1.5 + x = 34.673476895 Solving 1.5 + x = 34.673476895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 34.673476895 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 34.673476895 + -1.5 x = 34.673476895 + -1.5 Combine like terms: 34.673476895 + -1.5 = 33.173476895 x = 33.173476895 Simplifying x = 33.173476895Subproblem 2
x + 1.5 = -34.673476895 Simplifying x + 1.5 = -34.673476895 Reorder the terms: 1.5 + x = -34.673476895 Solving 1.5 + x = -34.673476895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -34.673476895 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -34.673476895 + -1.5 x = -34.673476895 + -1.5 Combine like terms: -34.673476895 + -1.5 = -36.173476895 x = -36.173476895 Simplifying x = -36.173476895Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.173476895, -36.173476895}
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