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Simplifying x2 + 54x + 576 = 0 Reorder the terms: 576 + 54x + x2 = 0 Solving 576 + 54x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-576' to each side of the equation. 576 + 54x + -576 + x2 = 0 + -576 Reorder the terms: 576 + -576 + 54x + x2 = 0 + -576 Combine like terms: 576 + -576 = 0 0 + 54x + x2 = 0 + -576 54x + x2 = 0 + -576 Combine like terms: 0 + -576 = -576 54x + x2 = -576 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 = -576 + 729 Reorder the terms: 729 + 54x + x2 = -576 + 729 Combine like terms: -576 + 729 = 153 729 + 54x + x2 = 153 Factor a perfect square on the left side: (x + 27)(x + 27) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (x + 27) equal to 12.369316877 and -12.369316877.Subproblem 1
x + 27 = 12.369316877 Simplifying x + 27 = 12.369316877 Reorder the terms: 27 + x = 12.369316877 Solving 27 + x = 12.369316877 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 = 12.369316877 + -27 Combine like terms: 27 + -27 = 0 0 + x = 12.369316877 + -27 x = 12.369316877 + -27 Combine like terms: 12.369316877 + -27 = -14.630683123 x = -14.630683123 Simplifying x = -14.630683123Subproblem 2
x + 27 = -12.369316877 Simplifying x + 27 = -12.369316877 Reorder the terms: 27 + x = -12.369316877 Solving 27 + x = -12.369316877 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 = -12.369316877 + -27 Combine like terms: 27 + -27 = 0 0 + x = -12.369316877 + -27 x = -12.369316877 + -27 Combine like terms: -12.369316877 + -27 = -39.369316877 x = -39.369316877 Simplifying x = -39.369316877Solution
The solution to the problem is based on the solutions from the subproblems. x = {-14.630683123, -39.369316877}
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