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Simplifying x2 + 54x + -72 = 0 Reorder the terms: -72 + 54x + x2 = 0 Solving -72 + 54x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 54x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 54x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 54x + x2 = 0 + 72 54x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 54x + x2 = 72 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 = 72 + 729 Reorder the terms: 729 + 54x + x2 = 72 + 729 Combine like terms: 72 + 729 = 801 729 + 54x + x2 = 801 Factor a perfect square on the left side: (x + 27)(x + 27) = 801 Calculate the square root of the right side: 28.301943396 Break this problem into two subproblems by setting (x + 27) equal to 28.301943396 and -28.301943396.Subproblem 1
x + 27 = 28.301943396 Simplifying x + 27 = 28.301943396 Reorder the terms: 27 + x = 28.301943396 Solving 27 + x = 28.301943396 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 = 28.301943396 + -27 Combine like terms: 27 + -27 = 0 0 + x = 28.301943396 + -27 x = 28.301943396 + -27 Combine like terms: 28.301943396 + -27 = 1.301943396 x = 1.301943396 Simplifying x = 1.301943396Subproblem 2
x + 27 = -28.301943396 Simplifying x + 27 = -28.301943396 Reorder the terms: 27 + x = -28.301943396 Solving 27 + x = -28.301943396 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 = -28.301943396 + -27 Combine like terms: 27 + -27 = 0 0 + x = -28.301943396 + -27 x = -28.301943396 + -27 Combine like terms: -28.301943396 + -27 = -55.301943396 x = -55.301943396 Simplifying x = -55.301943396Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.301943396, -55.301943396}
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