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Simplifying 2x2 + 5x + -104 = 0 Reorder the terms: -104 + 5x + 2x2 = 0 Solving -104 + 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'. -52 + 2.5x + x2 = 0 Move the constant term to the right: Add '52' to each side of the equation. -52 + 2.5x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + 2.5x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 2.5x + x2 = 0 + 52 2.5x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 2.5x + x2 = 52 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 = 52 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 52 + 1.5625 Combine like terms: 52 + 1.5625 = 53.5625 1.5625 + 2.5x + x2 = 53.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 53.5625 Calculate the square root of the right side: 7.318640584 Break this problem into two subproblems by setting (x + 1.25) equal to 7.318640584 and -7.318640584.Subproblem 1
x + 1.25 = 7.318640584 Simplifying x + 1.25 = 7.318640584 Reorder the terms: 1.25 + x = 7.318640584 Solving 1.25 + x = 7.318640584 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 = 7.318640584 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 7.318640584 + -1.25 x = 7.318640584 + -1.25 Combine like terms: 7.318640584 + -1.25 = 6.068640584 x = 6.068640584 Simplifying x = 6.068640584Subproblem 2
x + 1.25 = -7.318640584 Simplifying x + 1.25 = -7.318640584 Reorder the terms: 1.25 + x = -7.318640584 Solving 1.25 + x = -7.318640584 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 = -7.318640584 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -7.318640584 + -1.25 x = -7.318640584 + -1.25 Combine like terms: -7.318640584 + -1.25 = -8.568640584 x = -8.568640584 Simplifying x = -8.568640584Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.068640584, -8.568640584}
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