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Simplifying 2x2 + x + -268 = 0 Reorder the terms: -268 + x + 2x2 = 0 Solving -268 + x + 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'. -134 + 0.5x + x2 = 0 Move the constant term to the right: Add '134' to each side of the equation. -134 + 0.5x + 134 + x2 = 0 + 134 Reorder the terms: -134 + 134 + 0.5x + x2 = 0 + 134 Combine like terms: -134 + 134 = 0 0 + 0.5x + x2 = 0 + 134 0.5x + x2 = 0 + 134 Combine like terms: 0 + 134 = 134 0.5x + x2 = 134 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 134 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 134 + 0.25 Combine like terms: 134 + 0.25 = 134.25 0.25 + 0.5x + x2 = 134.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 134.25 Calculate the square root of the right side: 11.586630226 Break this problem into two subproblems by setting (x + 0.5) equal to 11.586630226 and -11.586630226.Subproblem 1
x + 0.5 = 11.586630226 Simplifying x + 0.5 = 11.586630226 Reorder the terms: 0.5 + x = 11.586630226 Solving 0.5 + x = 11.586630226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 11.586630226 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 11.586630226 + -0.5 x = 11.586630226 + -0.5 Combine like terms: 11.586630226 + -0.5 = 11.086630226 x = 11.086630226 Simplifying x = 11.086630226Subproblem 2
x + 0.5 = -11.586630226 Simplifying x + 0.5 = -11.586630226 Reorder the terms: 0.5 + x = -11.586630226 Solving 0.5 + x = -11.586630226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -11.586630226 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -11.586630226 + -0.5 x = -11.586630226 + -0.5 Combine like terms: -11.586630226 + -0.5 = -12.086630226 x = -12.086630226 Simplifying x = -12.086630226Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.086630226, -12.086630226}
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