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Simplifying 11x2 + 5x + -18 = 0 Reorder the terms: -18 + 5x + 11x2 = 0 Solving -18 + 5x + 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 + 0.4545454545x + x2 = 0 Move the constant term to the right: Add '1.636363636' to each side of the equation. -1.636363636 + 0.4545454545x + 1.636363636 + x2 = 0 + 1.636363636 Reorder the terms: -1.636363636 + 1.636363636 + 0.4545454545x + x2 = 0 + 1.636363636 Combine like terms: -1.636363636 + 1.636363636 = 0.000000000 0.000000000 + 0.4545454545x + x2 = 0 + 1.636363636 0.4545454545x + x2 = 0 + 1.636363636 Combine like terms: 0 + 1.636363636 = 1.636363636 0.4545454545x + x2 = 1.636363636 The x term is 0.4545454545x. Take half its coefficient (0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. 0.4545454545x + 0.05165289257 + x2 = 1.636363636 + 0.05165289257 Reorder the terms: 0.05165289257 + 0.4545454545x + x2 = 1.636363636 + 0.05165289257 Combine like terms: 1.636363636 + 0.05165289257 = 1.68801652857 0.05165289257 + 0.4545454545x + x2 = 1.68801652857 Factor a perfect square on the left side: (x + 0.2272727273)(x + 0.2272727273) = 1.68801652857 Calculate the square root of the right side: 1.299236902 Break this problem into two subproblems by setting (x + 0.2272727273) equal to 1.299236902 and -1.299236902.Subproblem 1
x + 0.2272727273 = 1.299236902 Simplifying x + 0.2272727273 = 1.299236902 Reorder the terms: 0.2272727273 + x = 1.299236902 Solving 0.2272727273 + x = 1.299236902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + x = 1.299236902 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = 1.299236902 + -0.2272727273 x = 1.299236902 + -0.2272727273 Combine like terms: 1.299236902 + -0.2272727273 = 1.0719641747 x = 1.0719641747 Simplifying x = 1.0719641747Subproblem 2
x + 0.2272727273 = -1.299236902 Simplifying x + 0.2272727273 = -1.299236902 Reorder the terms: 0.2272727273 + x = -1.299236902 Solving 0.2272727273 + x = -1.299236902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2272727273' to each side of the equation. 0.2272727273 + -0.2272727273 + x = -1.299236902 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + x = -1.299236902 + -0.2272727273 x = -1.299236902 + -0.2272727273 Combine like terms: -1.299236902 + -0.2272727273 = -1.5265096293 x = -1.5265096293 Simplifying x = -1.5265096293Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0719641747, -1.5265096293}
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