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Simplifying 11x2 + x + -2 = 0 Reorder the terms: -2 + x + 11x2 = 0 Solving -2 + x + 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'. -0.1818181818 + 0.09090909091x + x2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + 0.09090909091x + 0.1818181818 + x2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + 0.09090909091x + x2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + 0.09090909091x + x2 = 0 + 0.1818181818 0.09090909091x + x2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 0.09090909091x + x2 = 0.1818181818 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. 0.09090909091x + 0.25 + x2 = 0.1818181818 + 0.25 Reorder the terms: 0.25 + 0.09090909091x + x2 = 0.1818181818 + 0.25 Combine like terms: 0.1818181818 + 0.25 = 0.4318181818 0.25 + 0.09090909091x + x2 = 0.4318181818 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.4318181818 Calculate the square root of the right side: 0.657128741 Break this problem into two subproblems by setting (x + 0.5) equal to 0.657128741 and -0.657128741.Subproblem 1
x + 0.5 = 0.657128741 Simplifying x + 0.5 = 0.657128741 Reorder the terms: 0.5 + x = 0.657128741 Solving 0.5 + x = 0.657128741 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 = 0.657128741 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.657128741 + -0.5 x = 0.657128741 + -0.5 Combine like terms: 0.657128741 + -0.5 = 0.157128741 x = 0.157128741 Simplifying x = 0.157128741Subproblem 2
x + 0.5 = -0.657128741 Simplifying x + 0.5 = -0.657128741 Reorder the terms: 0.5 + x = -0.657128741 Solving 0.5 + x = -0.657128741 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 = -0.657128741 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.657128741 + -0.5 x = -0.657128741 + -0.5 Combine like terms: -0.657128741 + -0.5 = -1.157128741 x = -1.157128741 Simplifying x = -1.157128741Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.157128741, -1.157128741}
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