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Simplifying 11x2 + 2x + -154 = 0 Reorder the terms: -154 + 2x + 11x2 = 0 Solving -154 + 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'. -14 + 0.1818181818x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 0.1818181818x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 0.1818181818x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 0.1818181818x + x2 = 0 + 14 0.1818181818x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 0.1818181818x + x2 = 14 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 = 14 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818x + x2 = 14 + 0.008264462808 Combine like terms: 14 + 0.008264462808 = 14.008264462808 0.008264462808 + 0.1818181818x + x2 = 14.008264462808 Factor a perfect square on the left side: (x + 0.0909090909)(x + 0.0909090909) = 14.008264462808 Calculate the square root of the right side: 3.742761609 Break this problem into two subproblems by setting (x + 0.0909090909) equal to 3.742761609 and -3.742761609.Subproblem 1
x + 0.0909090909 = 3.742761609 Simplifying x + 0.0909090909 = 3.742761609 Reorder the terms: 0.0909090909 + x = 3.742761609 Solving 0.0909090909 + x = 3.742761609 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 = 3.742761609 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = 3.742761609 + -0.0909090909 x = 3.742761609 + -0.0909090909 Combine like terms: 3.742761609 + -0.0909090909 = 3.6518525181 x = 3.6518525181 Simplifying x = 3.6518525181Subproblem 2
x + 0.0909090909 = -3.742761609 Simplifying x + 0.0909090909 = -3.742761609 Reorder the terms: 0.0909090909 + x = -3.742761609 Solving 0.0909090909 + x = -3.742761609 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 = -3.742761609 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = -3.742761609 + -0.0909090909 x = -3.742761609 + -0.0909090909 Combine like terms: -3.742761609 + -0.0909090909 = -3.8336706999 x = -3.8336706999 Simplifying x = -3.8336706999Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.6518525181, -3.8336706999}
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