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Simplifying 11x2 = 2x + 18 Reorder the terms: 11x2 = 18 + 2x Solving 11x2 = 18 + 2x Solving for variable 'x'. Reorder the terms: -18 + -2x + 11x2 = 18 + 2x + -18 + -2x Reorder the terms: -18 + -2x + 11x2 = 18 + -18 + 2x + -2x Combine like terms: 18 + -18 = 0 -18 + -2x + 11x2 = 0 + 2x + -2x -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 = 1.3733396339 x = 1.3733396339 Simplifying x = 1.3733396339Subproblem 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 = -1.1915214521 x = -1.1915214521 Simplifying x = -1.1915214521Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3733396339, -1.1915214521}
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