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Simplifying x2 + 54x + -1584 = 0 Reorder the terms: -1584 + 54x + x2 = 0 Solving -1584 + 54x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1584' to each side of the equation. -1584 + 54x + 1584 + x2 = 0 + 1584 Reorder the terms: -1584 + 1584 + 54x + x2 = 0 + 1584 Combine like terms: -1584 + 1584 = 0 0 + 54x + x2 = 0 + 1584 54x + x2 = 0 + 1584 Combine like terms: 0 + 1584 = 1584 54x + x2 = 1584 The x term is 54x. Take half its coefficient (27). Square it (729) and add it to both sides. Add '729' to each side of the equation. 54x + 729 + x2 = 1584 + 729 Reorder the terms: 729 + 54x + x2 = 1584 + 729 Combine like terms: 1584 + 729 = 2313 729 + 54x + x2 = 2313 Factor a perfect square on the left side: (x + 27)(x + 27) = 2313 Calculate the square root of the right side: 48.093658626 Break this problem into two subproblems by setting (x + 27) equal to 48.093658626 and -48.093658626.Subproblem 1
x + 27 = 48.093658626 Simplifying x + 27 = 48.093658626 Reorder the terms: 27 + x = 48.093658626 Solving 27 + x = 48.093658626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = 48.093658626 + -27 Combine like terms: 27 + -27 = 0 0 + x = 48.093658626 + -27 x = 48.093658626 + -27 Combine like terms: 48.093658626 + -27 = 21.093658626 x = 21.093658626 Simplifying x = 21.093658626Subproblem 2
x + 27 = -48.093658626 Simplifying x + 27 = -48.093658626 Reorder the terms: 27 + x = -48.093658626 Solving 27 + x = -48.093658626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = -48.093658626 + -27 Combine like terms: 27 + -27 = 0 0 + x = -48.093658626 + -27 x = -48.093658626 + -27 Combine like terms: -48.093658626 + -27 = -75.093658626 x = -75.093658626 Simplifying x = -75.093658626Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.093658626, -75.093658626}
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