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Simplifying 2x2 + -5x + -54 = 0 Reorder the terms: -54 + -5x + 2x2 = 0 Solving -54 + -5x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -27 + -2.5x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -2.5x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -2.5x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -2.5x + x2 = 0 + 27 -2.5x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -2.5x + x2 = 27 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 27 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 27 + 1.5625 Combine like terms: 27 + 1.5625 = 28.5625 1.5625 + -2.5x + x2 = 28.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 28.5625 Calculate the square root of the right side: 5.344389582 Break this problem into two subproblems by setting (x + -1.25) equal to 5.344389582 and -5.344389582.Subproblem 1
x + -1.25 = 5.344389582 Simplifying x + -1.25 = 5.344389582 Reorder the terms: -1.25 + x = 5.344389582 Solving -1.25 + x = 5.344389582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 5.344389582 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 5.344389582 + 1.25 x = 5.344389582 + 1.25 Combine like terms: 5.344389582 + 1.25 = 6.594389582 x = 6.594389582 Simplifying x = 6.594389582Subproblem 2
x + -1.25 = -5.344389582 Simplifying x + -1.25 = -5.344389582 Reorder the terms: -1.25 + x = -5.344389582 Solving -1.25 + x = -5.344389582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -5.344389582 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -5.344389582 + 1.25 x = -5.344389582 + 1.25 Combine like terms: -5.344389582 + 1.25 = -4.094389582 x = -4.094389582 Simplifying x = -4.094389582Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.594389582, -4.094389582}
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