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Simplifying 11x2 + -97x + -2 = 0 Reorder the terms: -2 + -97x + 11x2 = 0 Solving -2 + -97x + 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 + -8.818181818x + x2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + -8.818181818x + 0.1818181818 + x2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + -8.818181818x + x2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + -8.818181818x + x2 = 0 + 0.1818181818 -8.818181818x + x2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 -8.818181818x + x2 = 0.1818181818 The x term is -8.818181818x. Take half its coefficient (-4.409090909). Square it (19.44008264) and add it to both sides. Add '19.44008264' to each side of the equation. -8.818181818x + 19.44008264 + x2 = 0.1818181818 + 19.44008264 Reorder the terms: 19.44008264 + -8.818181818x + x2 = 0.1818181818 + 19.44008264 Combine like terms: 0.1818181818 + 19.44008264 = 19.6219008218 19.44008264 + -8.818181818x + x2 = 19.6219008218 Factor a perfect square on the left side: (x + -4.409090909)(x + -4.409090909) = 19.6219008218 Calculate the square root of the right side: 4.429661479 Break this problem into two subproblems by setting (x + -4.409090909) equal to 4.429661479 and -4.429661479.Subproblem 1
x + -4.409090909 = 4.429661479 Simplifying x + -4.409090909 = 4.429661479 Reorder the terms: -4.409090909 + x = 4.429661479 Solving -4.409090909 + x = 4.429661479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.409090909' to each side of the equation. -4.409090909 + 4.409090909 + x = 4.429661479 + 4.409090909 Combine like terms: -4.409090909 + 4.409090909 = 0.000000000 0.000000000 + x = 4.429661479 + 4.409090909 x = 4.429661479 + 4.409090909 Combine like terms: 4.429661479 + 4.409090909 = 8.838752388 x = 8.838752388 Simplifying x = 8.838752388Subproblem 2
x + -4.409090909 = -4.429661479 Simplifying x + -4.409090909 = -4.429661479 Reorder the terms: -4.409090909 + x = -4.429661479 Solving -4.409090909 + x = -4.429661479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.409090909' to each side of the equation. -4.409090909 + 4.409090909 + x = -4.429661479 + 4.409090909 Combine like terms: -4.409090909 + 4.409090909 = 0.000000000 0.000000000 + x = -4.429661479 + 4.409090909 x = -4.429661479 + 4.409090909 Combine like terms: -4.429661479 + 4.409090909 = -0.02057057 x = -0.02057057 Simplifying x = -0.02057057Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.838752388, -0.02057057}
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