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Simplifying x2 = 10.8 + -54x Solving x2 = 10.8 + -54x Solving for variable 'x'. Reorder the terms: -10.8 + 54x + x2 = 10.8 + -54x + -10.8 + 54x Reorder the terms: -10.8 + 54x + x2 = 10.8 + -10.8 + -54x + 54x Combine like terms: 10.8 + -10.8 = 0.0 -10.8 + 54x + x2 = 0.0 + -54x + 54x -10.8 + 54x + x2 = -54x + 54x Combine like terms: -54x + 54x = 0 -10.8 + 54x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10.8' to each side of the equation. -10.8 + 54x + 10.8 + x2 = 0 + 10.8 Reorder the terms: -10.8 + 10.8 + 54x + x2 = 0 + 10.8 Combine like terms: -10.8 + 10.8 = 0.0 0.0 + 54x + x2 = 0 + 10.8 54x + x2 = 0 + 10.8 Combine like terms: 0 + 10.8 = 10.8 54x + x2 = 10.8 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 = 10.8 + 729 Reorder the terms: 729 + 54x + x2 = 10.8 + 729 Combine like terms: 10.8 + 729 = 739.8 729 + 54x + x2 = 739.8 Factor a perfect square on the left side: (x + 27)(x + 27) = 739.8 Calculate the square root of the right side: 27.199264696 Break this problem into two subproblems by setting (x + 27) equal to 27.199264696 and -27.199264696.Subproblem 1
x + 27 = 27.199264696 Simplifying x + 27 = 27.199264696 Reorder the terms: 27 + x = 27.199264696 Solving 27 + x = 27.199264696 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 = 27.199264696 + -27 Combine like terms: 27 + -27 = 0 0 + x = 27.199264696 + -27 x = 27.199264696 + -27 Combine like terms: 27.199264696 + -27 = 0.199264696 x = 0.199264696 Simplifying x = 0.199264696Subproblem 2
x + 27 = -27.199264696 Simplifying x + 27 = -27.199264696 Reorder the terms: 27 + x = -27.199264696 Solving 27 + x = -27.199264696 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 = -27.199264696 + -27 Combine like terms: 27 + -27 = 0 0 + x = -27.199264696 + -27 x = -27.199264696 + -27 Combine like terms: -27.199264696 + -27 = -54.199264696 x = -54.199264696 Simplifying x = -54.199264696Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.199264696, -54.199264696}
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