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Simplifying -11x2 + 4x + 18 = 0 Reorder the terms: 18 + 4x + -11x2 = 0 Solving 18 + 4x + -11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -1.636363636 + -0.3636363636x + x2 = 0 Move the constant term to the right: Add '1.636363636' to each side of the equation. -1.636363636 + -0.3636363636x + 1.636363636 + x2 = 0 + 1.636363636 Reorder the terms: -1.636363636 + 1.636363636 + -0.3636363636x + x2 = 0 + 1.636363636 Combine like terms: -1.636363636 + 1.636363636 = 0.000000000 0.000000000 + -0.3636363636x + x2 = 0 + 1.636363636 -0.3636363636x + x2 = 0 + 1.636363636 Combine like terms: 0 + 1.636363636 = 1.636363636 -0.3636363636x + x2 = 1.636363636 The x term is -0.3636363636x. Take half its coefficient (-0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. -0.3636363636x + 0.03305785123 + x2 = 1.636363636 + 0.03305785123 Reorder the terms: 0.03305785123 + -0.3636363636x + x2 = 1.636363636 + 0.03305785123 Combine like terms: 1.636363636 + 0.03305785123 = 1.66942148723 0.03305785123 + -0.3636363636x + x2 = 1.66942148723 Factor a perfect square on the left side: (x + -0.1818181818)(x + -0.1818181818) = 1.66942148723 Calculate the square root of the right side: 1.292060946 Break this problem into two subproblems by setting (x + -0.1818181818) equal to 1.292060946 and -1.292060946.Subproblem 1
x + -0.1818181818 = 1.292060946 Simplifying x + -0.1818181818 = 1.292060946 Reorder the terms: -0.1818181818 + x = 1.292060946 Solving -0.1818181818 + x = 1.292060946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + x = 1.292060946 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = 1.292060946 + 0.1818181818 x = 1.292060946 + 0.1818181818 Combine like terms: 1.292060946 + 0.1818181818 = 1.4738791278 x = 1.4738791278 Simplifying x = 1.4738791278Subproblem 2
x + -0.1818181818 = -1.292060946 Simplifying x + -0.1818181818 = -1.292060946 Reorder the terms: -0.1818181818 + x = -1.292060946 Solving -0.1818181818 + x = -1.292060946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.1818181818 + x = -1.292060946 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = -1.292060946 + 0.1818181818 x = -1.292060946 + 0.1818181818 Combine like terms: -1.292060946 + 0.1818181818 = -1.1102427642 x = -1.1102427642 Simplifying x = -1.1102427642Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4738791278, -1.1102427642}
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