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Simplifying 2x2 + x = 405 Reorder the terms: x + 2x2 = 405 Solving x + 2x2 = 405 Solving for variable 'x'. Reorder the terms: -405 + x + 2x2 = 405 + -405 Combine like terms: 405 + -405 = 0 -405 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -202.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '202.5' to each side of the equation. -202.5 + 0.5x + 202.5 + x2 = 0 + 202.5 Reorder the terms: -202.5 + 202.5 + 0.5x + x2 = 0 + 202.5 Combine like terms: -202.5 + 202.5 = 0.0 0.0 + 0.5x + x2 = 0 + 202.5 0.5x + x2 = 0 + 202.5 Combine like terms: 0 + 202.5 = 202.5 0.5x + x2 = 202.5 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 = 202.5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 202.5 + 0.25 Combine like terms: 202.5 + 0.25 = 202.75 0.25 + 0.5x + x2 = 202.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 202.75 Calculate the square root of the right side: 14.239030866 Break this problem into two subproblems by setting (x + 0.5) equal to 14.239030866 and -14.239030866.Subproblem 1
x + 0.5 = 14.239030866 Simplifying x + 0.5 = 14.239030866 Reorder the terms: 0.5 + x = 14.239030866 Solving 0.5 + x = 14.239030866 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 = 14.239030866 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 14.239030866 + -0.5 x = 14.239030866 + -0.5 Combine like terms: 14.239030866 + -0.5 = 13.739030866 x = 13.739030866 Simplifying x = 13.739030866Subproblem 2
x + 0.5 = -14.239030866 Simplifying x + 0.5 = -14.239030866 Reorder the terms: 0.5 + x = -14.239030866 Solving 0.5 + x = -14.239030866 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 = -14.239030866 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -14.239030866 + -0.5 x = -14.239030866 + -0.5 Combine like terms: -14.239030866 + -0.5 = -14.739030866 x = -14.739030866 Simplifying x = -14.739030866Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.739030866, -14.739030866}
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