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Simplifying 11x2 + 4x = 20 Reorder the terms: 4x + 11x2 = 20 Solving 4x + 11x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 4x + 11x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 4x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.818181818 + 0.3636363636x + x2 = 0 Move the constant term to the right: Add '1.818181818' to each side of the equation. -1.818181818 + 0.3636363636x + 1.818181818 + x2 = 0 + 1.818181818 Reorder the terms: -1.818181818 + 1.818181818 + 0.3636363636x + x2 = 0 + 1.818181818 Combine like terms: -1.818181818 + 1.818181818 = 0.000000000 0.000000000 + 0.3636363636x + x2 = 0 + 1.818181818 0.3636363636x + x2 = 0 + 1.818181818 Combine like terms: 0 + 1.818181818 = 1.818181818 0.3636363636x + x2 = 1.818181818 The x term is 0.3636363636x. Take half its coefficient (0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. 0.3636363636x + 0.03305785123 + x2 = 1.818181818 + 0.03305785123 Reorder the terms: 0.03305785123 + 0.3636363636x + x2 = 1.818181818 + 0.03305785123 Combine like terms: 1.818181818 + 0.03305785123 = 1.85123966923 0.03305785123 + 0.3636363636x + x2 = 1.85123966923 Factor a perfect square on the left side: (x + 0.1818181818)(x + 0.1818181818) = 1.85123966923 Calculate the square root of the right side: 1.360602686 Break this problem into two subproblems by setting (x + 0.1818181818) equal to 1.360602686 and -1.360602686.Subproblem 1
x + 0.1818181818 = 1.360602686 Simplifying x + 0.1818181818 = 1.360602686 Reorder the terms: 0.1818181818 + x = 1.360602686 Solving 0.1818181818 + x = 1.360602686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + x = 1.360602686 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = 1.360602686 + -0.1818181818 x = 1.360602686 + -0.1818181818 Combine like terms: 1.360602686 + -0.1818181818 = 1.1787845042 x = 1.1787845042 Simplifying x = 1.1787845042Subproblem 2
x + 0.1818181818 = -1.360602686 Simplifying x + 0.1818181818 = -1.360602686 Reorder the terms: 0.1818181818 + x = -1.360602686 Solving 0.1818181818 + x = -1.360602686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + x = -1.360602686 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = -1.360602686 + -0.1818181818 x = -1.360602686 + -0.1818181818 Combine like terms: -1.360602686 + -0.1818181818 = -1.5424208678 x = -1.5424208678 Simplifying x = -1.5424208678Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1787845042, -1.5424208678}
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