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Simplifying 2x2 + 25x + -168 = 0 Reorder the terms: -168 + 25x + 2x2 = 0 Solving -168 + 25x + 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'. -84 + 12.5x + x2 = 0 Move the constant term to the right: Add '84' to each side of the equation. -84 + 12.5x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + 12.5x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 12.5x + x2 = 0 + 84 12.5x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 12.5x + x2 = 84 The x term is 12.5x. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5x + 39.0625 + x2 = 84 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = 84 + 39.0625 Combine like terms: 84 + 39.0625 = 123.0625 39.0625 + 12.5x + x2 = 123.0625 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 123.0625 Calculate the square root of the right side: 11.093353866 Break this problem into two subproblems by setting (x + 6.25) equal to 11.093353866 and -11.093353866.Subproblem 1
x + 6.25 = 11.093353866 Simplifying x + 6.25 = 11.093353866 Reorder the terms: 6.25 + x = 11.093353866 Solving 6.25 + x = 11.093353866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = 11.093353866 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 11.093353866 + -6.25 x = 11.093353866 + -6.25 Combine like terms: 11.093353866 + -6.25 = 4.843353866 x = 4.843353866 Simplifying x = 4.843353866Subproblem 2
x + 6.25 = -11.093353866 Simplifying x + 6.25 = -11.093353866 Reorder the terms: 6.25 + x = -11.093353866 Solving 6.25 + x = -11.093353866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = -11.093353866 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -11.093353866 + -6.25 x = -11.093353866 + -6.25 Combine like terms: -11.093353866 + -6.25 = -17.343353866 x = -17.343353866 Simplifying x = -17.343353866Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.843353866, -17.343353866}
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