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Simplifying -1x2 + 54x + -222 = 0 Reorder the terms: -222 + 54x + -1x2 = 0 Solving -222 + 54x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 222 + -54x + x2 = 0 Move the constant term to the right: Add '-222' to each side of the equation. 222 + -54x + -222 + x2 = 0 + -222 Reorder the terms: 222 + -222 + -54x + x2 = 0 + -222 Combine like terms: 222 + -222 = 0 0 + -54x + x2 = 0 + -222 -54x + x2 = 0 + -222 Combine like terms: 0 + -222 = -222 -54x + x2 = -222 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 = -222 + 729 Reorder the terms: 729 + -54x + x2 = -222 + 729 Combine like terms: -222 + 729 = 507 729 + -54x + x2 = 507 Factor a perfect square on the left side: (x + -27)(x + -27) = 507 Calculate the square root of the right side: 22.516660498 Break this problem into two subproblems by setting (x + -27) equal to 22.516660498 and -22.516660498.Subproblem 1
x + -27 = 22.516660498 Simplifying x + -27 = 22.516660498 Reorder the terms: -27 + x = 22.516660498 Solving -27 + x = 22.516660498 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 = 22.516660498 + 27 Combine like terms: -27 + 27 = 0 0 + x = 22.516660498 + 27 x = 22.516660498 + 27 Combine like terms: 22.516660498 + 27 = 49.516660498 x = 49.516660498 Simplifying x = 49.516660498Subproblem 2
x + -27 = -22.516660498 Simplifying x + -27 = -22.516660498 Reorder the terms: -27 + x = -22.516660498 Solving -27 + x = -22.516660498 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 = -22.516660498 + 27 Combine like terms: -27 + 27 = 0 0 + x = -22.516660498 + 27 x = -22.516660498 + 27 Combine like terms: -22.516660498 + 27 = 4.483339502 x = 4.483339502 Simplifying x = 4.483339502Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.516660498, 4.483339502}
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