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Simplifying 11x2 + -2x + -14 = 0 Reorder the terms: -14 + -2x + 11x2 = 0 Solving -14 + -2x + 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'. -1.272727273 + -0.1818181818x + x2 = 0 Move the constant term to the right: Add '1.272727273' to each side of the equation. -1.272727273 + -0.1818181818x + 1.272727273 + x2 = 0 + 1.272727273 Reorder the terms: -1.272727273 + 1.272727273 + -0.1818181818x + x2 = 0 + 1.272727273 Combine like terms: -1.272727273 + 1.272727273 = 0.000000000 0.000000000 + -0.1818181818x + x2 = 0 + 1.272727273 -0.1818181818x + x2 = 0 + 1.272727273 Combine like terms: 0 + 1.272727273 = 1.272727273 -0.1818181818x + x2 = 1.272727273 The x term is -0.1818181818x. Take half its coefficient (-0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. -0.1818181818x + 0.008264462808 + x2 = 1.272727273 + 0.008264462808 Reorder the terms: 0.008264462808 + -0.1818181818x + x2 = 1.272727273 + 0.008264462808 Combine like terms: 1.272727273 + 0.008264462808 = 1.280991735808 0.008264462808 + -0.1818181818x + x2 = 1.280991735808 Factor a perfect square on the left side: (x + -0.0909090909)(x + -0.0909090909) = 1.280991735808 Calculate the square root of the right side: 1.131809054 Break this problem into two subproblems by setting (x + -0.0909090909) equal to 1.131809054 and -1.131809054.Subproblem 1
x + -0.0909090909 = 1.131809054 Simplifying x + -0.0909090909 = 1.131809054 Reorder the terms: -0.0909090909 + x = 1.131809054 Solving -0.0909090909 + x = 1.131809054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + x = 1.131809054 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = 1.131809054 + 0.0909090909 x = 1.131809054 + 0.0909090909 Combine like terms: 1.131809054 + 0.0909090909 = 1.2227181449 x = 1.2227181449 Simplifying x = 1.2227181449Subproblem 2
x + -0.0909090909 = -1.131809054 Simplifying x + -0.0909090909 = -1.131809054 Reorder the terms: -0.0909090909 + x = -1.131809054 Solving -0.0909090909 + x = -1.131809054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + x = -1.131809054 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = -1.131809054 + 0.0909090909 x = -1.131809054 + 0.0909090909 Combine like terms: -1.131809054 + 0.0909090909 = -1.0408999631 x = -1.0408999631 Simplifying x = -1.0408999631Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2227181449, -1.0408999631}
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