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Simplifying 11x2 + -4x = 12 Reorder the terms: -4x + 11x2 = 12 Solving -4x + 11x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + -4x + 11x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -4x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.090909091 + -0.3636363636x + x2 = 0 Move the constant term to the right: Add '1.090909091' to each side of the equation. -1.090909091 + -0.3636363636x + 1.090909091 + x2 = 0 + 1.090909091 Reorder the terms: -1.090909091 + 1.090909091 + -0.3636363636x + x2 = 0 + 1.090909091 Combine like terms: -1.090909091 + 1.090909091 = 0.000000000 0.000000000 + -0.3636363636x + x2 = 0 + 1.090909091 -0.3636363636x + x2 = 0 + 1.090909091 Combine like terms: 0 + 1.090909091 = 1.090909091 -0.3636363636x + x2 = 1.090909091 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 = 1.090909091 + 0.03305785123 Reorder the terms: 0.03305785123 + -0.3636363636x + x2 = 1.090909091 + 0.03305785123 Combine like terms: 1.090909091 + 0.03305785123 = 1.12396694223 0.03305785123 + -0.3636363636x + x2 = 1.12396694223 Factor a perfect square on the left side: (x + -0.1818181818)(x + -0.1818181818) = 1.12396694223 Calculate the square root of the right side: 1.060173072 Break this problem into two subproblems by setting (x + -0.1818181818) equal to 1.060173072 and -1.060173072.Subproblem 1
x + -0.1818181818 = 1.060173072 Simplifying x + -0.1818181818 = 1.060173072 Reorder the terms: -0.1818181818 + x = 1.060173072 Solving -0.1818181818 + x = 1.060173072 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 = 1.060173072 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = 1.060173072 + 0.1818181818 x = 1.060173072 + 0.1818181818 Combine like terms: 1.060173072 + 0.1818181818 = 1.2419912538 x = 1.2419912538 Simplifying x = 1.2419912538Subproblem 2
x + -0.1818181818 = -1.060173072 Simplifying x + -0.1818181818 = -1.060173072 Reorder the terms: -0.1818181818 + x = -1.060173072 Solving -0.1818181818 + x = -1.060173072 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 = -1.060173072 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + x = -1.060173072 + 0.1818181818 x = -1.060173072 + 0.1818181818 Combine like terms: -1.060173072 + 0.1818181818 = -0.8783548902 x = -0.8783548902 Simplifying x = -0.8783548902Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2419912538, -0.8783548902}
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