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Simplifying 2x2 + 23x + -2 = 0 Reorder the terms: -2 + 23x + 2x2 = 0 Solving -2 + 23x + 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'. -1 + 11.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 11.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 11.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 11.5x + x2 = 0 + 1 11.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 11.5x + x2 = 1 The x term is 11.5x. Take half its coefficient (5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. 11.5x + 33.0625 + x2 = 1 + 33.0625 Reorder the terms: 33.0625 + 11.5x + x2 = 1 + 33.0625 Combine like terms: 1 + 33.0625 = 34.0625 33.0625 + 11.5x + x2 = 34.0625 Factor a perfect square on the left side: (x + 5.75)(x + 5.75) = 34.0625 Calculate the square root of the right side: 5.836308765 Break this problem into two subproblems by setting (x + 5.75) equal to 5.836308765 and -5.836308765.Subproblem 1
x + 5.75 = 5.836308765 Simplifying x + 5.75 = 5.836308765 Reorder the terms: 5.75 + x = 5.836308765 Solving 5.75 + x = 5.836308765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = 5.836308765 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = 5.836308765 + -5.75 x = 5.836308765 + -5.75 Combine like terms: 5.836308765 + -5.75 = 0.086308765 x = 0.086308765 Simplifying x = 0.086308765Subproblem 2
x + 5.75 = -5.836308765 Simplifying x + 5.75 = -5.836308765 Reorder the terms: 5.75 + x = -5.836308765 Solving 5.75 + x = -5.836308765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = -5.836308765 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = -5.836308765 + -5.75 x = -5.836308765 + -5.75 Combine like terms: -5.836308765 + -5.75 = -11.586308765 x = -11.586308765 Simplifying x = -11.586308765Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.086308765, -11.586308765}
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