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Simplifying x2 + 54x + -85 = 0 Reorder the terms: -85 + 54x + x2 = 0 Solving -85 + 54x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + 54x + 85 + x2 = 0 + 85 Reorder the terms: -85 + 85 + 54x + x2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + 54x + x2 = 0 + 85 54x + x2 = 0 + 85 Combine like terms: 0 + 85 = 85 54x + x2 = 85 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 = 85 + 729 Reorder the terms: 729 + 54x + x2 = 85 + 729 Combine like terms: 85 + 729 = 814 729 + 54x + x2 = 814 Factor a perfect square on the left side: (x + 27)(x + 27) = 814 Calculate the square root of the right side: 28.530685235 Break this problem into two subproblems by setting (x + 27) equal to 28.530685235 and -28.530685235.Subproblem 1
x + 27 = 28.530685235 Simplifying x + 27 = 28.530685235 Reorder the terms: 27 + x = 28.530685235 Solving 27 + x = 28.530685235 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 = 28.530685235 + -27 Combine like terms: 27 + -27 = 0 0 + x = 28.530685235 + -27 x = 28.530685235 + -27 Combine like terms: 28.530685235 + -27 = 1.530685235 x = 1.530685235 Simplifying x = 1.530685235Subproblem 2
x + 27 = -28.530685235 Simplifying x + 27 = -28.530685235 Reorder the terms: 27 + x = -28.530685235 Solving 27 + x = -28.530685235 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 = -28.530685235 + -27 Combine like terms: 27 + -27 = 0 0 + x = -28.530685235 + -27 x = -28.530685235 + -27 Combine like terms: -28.530685235 + -27 = -55.530685235 x = -55.530685235 Simplifying x = -55.530685235Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.530685235, -55.530685235}
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