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Simplifying 11x2 = 7 + -2x Solving 11x2 = 7 + -2x Solving for variable 'x'. Reorder the terms: -7 + 2x + 11x2 = 7 + -2x + -7 + 2x Reorder the terms: -7 + 2x + 11x2 = 7 + -7 + -2x + 2x Combine like terms: 7 + -7 = 0 -7 + 2x + 11x2 = 0 + -2x + 2x -7 + 2x + 11x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -7 + 2x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.6363636364 + 0.1818181818x + x2 = 0 Move the constant term to the right: Add '0.6363636364' to each side of the equation. -0.6363636364 + 0.1818181818x + 0.6363636364 + x2 = 0 + 0.6363636364 Reorder the terms: -0.6363636364 + 0.6363636364 + 0.1818181818x + x2 = 0 + 0.6363636364 Combine like terms: -0.6363636364 + 0.6363636364 = 0.0000000000 0.0000000000 + 0.1818181818x + x2 = 0 + 0.6363636364 0.1818181818x + x2 = 0 + 0.6363636364 Combine like terms: 0 + 0.6363636364 = 0.6363636364 0.1818181818x + x2 = 0.6363636364 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 = 0.6363636364 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818x + x2 = 0.6363636364 + 0.008264462808 Combine like terms: 0.6363636364 + 0.008264462808 = 0.644628099208 0.008264462808 + 0.1818181818x + x2 = 0.644628099208 Factor a perfect square on the left side: (x + 0.0909090909)(x + 0.0909090909) = 0.644628099208 Calculate the square root of the right side: 0.802887352 Break this problem into two subproblems by setting (x + 0.0909090909) equal to 0.802887352 and -0.802887352.Subproblem 1
x + 0.0909090909 = 0.802887352 Simplifying x + 0.0909090909 = 0.802887352 Reorder the terms: 0.0909090909 + x = 0.802887352 Solving 0.0909090909 + x = 0.802887352 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 = 0.802887352 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = 0.802887352 + -0.0909090909 x = 0.802887352 + -0.0909090909 Combine like terms: 0.802887352 + -0.0909090909 = 0.7119782611 x = 0.7119782611 Simplifying x = 0.7119782611Subproblem 2
x + 0.0909090909 = -0.802887352 Simplifying x + 0.0909090909 = -0.802887352 Reorder the terms: 0.0909090909 + x = -0.802887352 Solving 0.0909090909 + x = -0.802887352 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 = -0.802887352 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = -0.802887352 + -0.0909090909 x = -0.802887352 + -0.0909090909 Combine like terms: -0.802887352 + -0.0909090909 = -0.8937964429 x = -0.8937964429 Simplifying x = -0.8937964429Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7119782611, -0.8937964429}
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