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Simplifying 11x2 + -7x + -40 = 0 Reorder the terms: -40 + -7x + 11x2 = 0 Solving -40 + -7x + 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'. -3.636363636 + -0.6363636364x + x2 = 0 Move the constant term to the right: Add '3.636363636' to each side of the equation. -3.636363636 + -0.6363636364x + 3.636363636 + x2 = 0 + 3.636363636 Reorder the terms: -3.636363636 + 3.636363636 + -0.6363636364x + x2 = 0 + 3.636363636 Combine like terms: -3.636363636 + 3.636363636 = 0.000000000 0.000000000 + -0.6363636364x + x2 = 0 + 3.636363636 -0.6363636364x + x2 = 0 + 3.636363636 Combine like terms: 0 + 3.636363636 = 3.636363636 -0.6363636364x + x2 = 3.636363636 The x term is -0.6363636364x. Take half its coefficient (-0.3181818182). Square it (0.1012396694) and add it to both sides. Add '0.1012396694' to each side of the equation. -0.6363636364x + 0.1012396694 + x2 = 3.636363636 + 0.1012396694 Reorder the terms: 0.1012396694 + -0.6363636364x + x2 = 3.636363636 + 0.1012396694 Combine like terms: 3.636363636 + 0.1012396694 = 3.7376033054 0.1012396694 + -0.6363636364x + x2 = 3.7376033054 Factor a perfect square on the left side: (x + -0.3181818182)(x + -0.3181818182) = 3.7376033054 Calculate the square root of the right side: 1.933288211 Break this problem into two subproblems by setting (x + -0.3181818182) equal to 1.933288211 and -1.933288211.Subproblem 1
x + -0.3181818182 = 1.933288211 Simplifying x + -0.3181818182 = 1.933288211 Reorder the terms: -0.3181818182 + x = 1.933288211 Solving -0.3181818182 + x = 1.933288211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + x = 1.933288211 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = 1.933288211 + 0.3181818182 x = 1.933288211 + 0.3181818182 Combine like terms: 1.933288211 + 0.3181818182 = 2.2514700292 x = 2.2514700292 Simplifying x = 2.2514700292Subproblem 2
x + -0.3181818182 = -1.933288211 Simplifying x + -0.3181818182 = -1.933288211 Reorder the terms: -0.3181818182 + x = -1.933288211 Solving -0.3181818182 + x = -1.933288211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + x = -1.933288211 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = -1.933288211 + 0.3181818182 x = -1.933288211 + 0.3181818182 Combine like terms: -1.933288211 + 0.3181818182 = -1.6151063928 x = -1.6151063928 Simplifying x = -1.6151063928Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2514700292, -1.6151063928}
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