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Simplifying 11x2 + -18 = -2x Reorder the terms: -18 + 11x2 = -2x Solving -18 + 11x2 = -2x Solving for variable 'x'. Reorder the terms: -18 + 2x + 11x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -18 + 2x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.636363636 + 0.1818181818x + x2 = 0 Move the constant term to the right: Add '1.636363636' to each side of the equation. -1.636363636 + 0.1818181818x + 1.636363636 + x2 = 0 + 1.636363636 Reorder the terms: -1.636363636 + 1.636363636 + 0.1818181818x + x2 = 0 + 1.636363636 Combine like terms: -1.636363636 + 1.636363636 = 0.000000000 0.000000000 + 0.1818181818x + x2 = 0 + 1.636363636 0.1818181818x + x2 = 0 + 1.636363636 Combine like terms: 0 + 1.636363636 = 1.636363636 0.1818181818x + x2 = 1.636363636 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 = 1.636363636 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818x + x2 = 1.636363636 + 0.008264462808 Combine like terms: 1.636363636 + 0.008264462808 = 1.644628098808 0.008264462808 + 0.1818181818x + x2 = 1.644628098808 Factor a perfect square on the left side: (x + 0.0909090909)(x + 0.0909090909) = 1.644628098808 Calculate the square root of the right side: 1.282430543 Break this problem into two subproblems by setting (x + 0.0909090909) equal to 1.282430543 and -1.282430543.Subproblem 1
x + 0.0909090909 = 1.282430543 Simplifying x + 0.0909090909 = 1.282430543 Reorder the terms: 0.0909090909 + x = 1.282430543 Solving 0.0909090909 + x = 1.282430543 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 = 1.282430543 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = 1.282430543 + -0.0909090909 x = 1.282430543 + -0.0909090909 Combine like terms: 1.282430543 + -0.0909090909 = 1.1915214521 x = 1.1915214521 Simplifying x = 1.1915214521Subproblem 2
x + 0.0909090909 = -1.282430543 Simplifying x + 0.0909090909 = -1.282430543 Reorder the terms: 0.0909090909 + x = -1.282430543 Solving 0.0909090909 + x = -1.282430543 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 = -1.282430543 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = -1.282430543 + -0.0909090909 x = -1.282430543 + -0.0909090909 Combine like terms: -1.282430543 + -0.0909090909 = -1.3733396339 x = -1.3733396339 Simplifying x = -1.3733396339Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1915214521, -1.3733396339}
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