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Simplifying 2x2 + 49x + -81 = 0 Reorder the terms: -81 + 49x + 2x2 = 0 Solving -81 + 49x + 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'. -40.5 + 24.5x + x2 = 0 Move the constant term to the right: Add '40.5' to each side of the equation. -40.5 + 24.5x + 40.5 + x2 = 0 + 40.5 Reorder the terms: -40.5 + 40.5 + 24.5x + x2 = 0 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + 24.5x + x2 = 0 + 40.5 24.5x + x2 = 0 + 40.5 Combine like terms: 0 + 40.5 = 40.5 24.5x + x2 = 40.5 The x term is 24.5x. Take half its coefficient (12.25). Square it (150.0625) and add it to both sides. Add '150.0625' to each side of the equation. 24.5x + 150.0625 + x2 = 40.5 + 150.0625 Reorder the terms: 150.0625 + 24.5x + x2 = 40.5 + 150.0625 Combine like terms: 40.5 + 150.0625 = 190.5625 150.0625 + 24.5x + x2 = 190.5625 Factor a perfect square on the left side: (x + 12.25)(x + 12.25) = 190.5625 Calculate the square root of the right side: 13.804437692 Break this problem into two subproblems by setting (x + 12.25) equal to 13.804437692 and -13.804437692.Subproblem 1
x + 12.25 = 13.804437692 Simplifying x + 12.25 = 13.804437692 Reorder the terms: 12.25 + x = 13.804437692 Solving 12.25 + x = 13.804437692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.25' to each side of the equation. 12.25 + -12.25 + x = 13.804437692 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + x = 13.804437692 + -12.25 x = 13.804437692 + -12.25 Combine like terms: 13.804437692 + -12.25 = 1.554437692 x = 1.554437692 Simplifying x = 1.554437692Subproblem 2
x + 12.25 = -13.804437692 Simplifying x + 12.25 = -13.804437692 Reorder the terms: 12.25 + x = -13.804437692 Solving 12.25 + x = -13.804437692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.25' to each side of the equation. 12.25 + -12.25 + x = -13.804437692 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + x = -13.804437692 + -12.25 x = -13.804437692 + -12.25 Combine like terms: -13.804437692 + -12.25 = -26.054437692 x = -26.054437692 Simplifying x = -26.054437692Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.554437692, -26.054437692}
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