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Simplifying x2 + 6x + -2448 = 0 Reorder the terms: -2448 + 6x + x2 = 0 Solving -2448 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2448' to each side of the equation. -2448 + 6x + 2448 + x2 = 0 + 2448 Reorder the terms: -2448 + 2448 + 6x + x2 = 0 + 2448 Combine like terms: -2448 + 2448 = 0 0 + 6x + x2 = 0 + 2448 6x + x2 = 0 + 2448 Combine like terms: 0 + 2448 = 2448 6x + x2 = 2448 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 2448 + 9 Reorder the terms: 9 + 6x + x2 = 2448 + 9 Combine like terms: 2448 + 9 = 2457 9 + 6x + x2 = 2457 Factor a perfect square on the left side: (x + 3)(x + 3) = 2457 Calculate the square root of the right side: 49.568134926 Break this problem into two subproblems by setting (x + 3) equal to 49.568134926 and -49.568134926.Subproblem 1
x + 3 = 49.568134926 Simplifying x + 3 = 49.568134926 Reorder the terms: 3 + x = 49.568134926 Solving 3 + x = 49.568134926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 49.568134926 + -3 Combine like terms: 3 + -3 = 0 0 + x = 49.568134926 + -3 x = 49.568134926 + -3 Combine like terms: 49.568134926 + -3 = 46.568134926 x = 46.568134926 Simplifying x = 46.568134926Subproblem 2
x + 3 = -49.568134926 Simplifying x + 3 = -49.568134926 Reorder the terms: 3 + x = -49.568134926 Solving 3 + x = -49.568134926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -49.568134926 + -3 Combine like terms: 3 + -3 = 0 0 + x = -49.568134926 + -3 x = -49.568134926 + -3 Combine like terms: -49.568134926 + -3 = -52.568134926 x = -52.568134926 Simplifying x = -52.568134926Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.568134926, -52.568134926}
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