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Simplifying 4(3x + -3) + -11x(x + -2) = 0 Reorder the terms: 4(-3 + 3x) + -11x(x + -2) = 0 (-3 * 4 + 3x * 4) + -11x(x + -2) = 0 (-12 + 12x) + -11x(x + -2) = 0 Reorder the terms: -12 + 12x + -11x(-2 + x) = 0 -12 + 12x + (-2 * -11x + x * -11x) = 0 -12 + 12x + (22x + -11x2) = 0 Combine like terms: 12x + 22x = 34x -12 + 34x + -11x2 = 0 Solving -12 + 34x + -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'. 1.090909091 + -3.090909091x + x2 = 0 Move the constant term to the right: Add '-1.090909091' to each side of the equation. 1.090909091 + -3.090909091x + -1.090909091 + x2 = 0 + -1.090909091 Reorder the terms: 1.090909091 + -1.090909091 + -3.090909091x + x2 = 0 + -1.090909091 Combine like terms: 1.090909091 + -1.090909091 = 0.000000000 0.000000000 + -3.090909091x + x2 = 0 + -1.090909091 -3.090909091x + x2 = 0 + -1.090909091 Combine like terms: 0 + -1.090909091 = -1.090909091 -3.090909091x + x2 = -1.090909091 The x term is -3.090909091x. Take half its coefficient (-1.545454546). Square it (2.388429754) and add it to both sides. Add '2.388429754' to each side of the equation. -3.090909091x + 2.388429754 + x2 = -1.090909091 + 2.388429754 Reorder the terms: 2.388429754 + -3.090909091x + x2 = -1.090909091 + 2.388429754 Combine like terms: -1.090909091 + 2.388429754 = 1.297520663 2.388429754 + -3.090909091x + x2 = 1.297520663 Factor a perfect square on the left side: (x + -1.545454546)(x + -1.545454546) = 1.297520663 Calculate the square root of the right side: 1.139087645 Break this problem into two subproblems by setting (x + -1.545454546) equal to 1.139087645 and -1.139087645.Subproblem 1
x + -1.545454546 = 1.139087645 Simplifying x + -1.545454546 = 1.139087645 Reorder the terms: -1.545454546 + x = 1.139087645 Solving -1.545454546 + x = 1.139087645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.545454546' to each side of the equation. -1.545454546 + 1.545454546 + x = 1.139087645 + 1.545454546 Combine like terms: -1.545454546 + 1.545454546 = 0.000000000 0.000000000 + x = 1.139087645 + 1.545454546 x = 1.139087645 + 1.545454546 Combine like terms: 1.139087645 + 1.545454546 = 2.684542191 x = 2.684542191 Simplifying x = 2.684542191Subproblem 2
x + -1.545454546 = -1.139087645 Simplifying x + -1.545454546 = -1.139087645 Reorder the terms: -1.545454546 + x = -1.139087645 Solving -1.545454546 + x = -1.139087645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.545454546' to each side of the equation. -1.545454546 + 1.545454546 + x = -1.139087645 + 1.545454546 Combine like terms: -1.545454546 + 1.545454546 = 0.000000000 0.000000000 + x = -1.139087645 + 1.545454546 x = -1.139087645 + 1.545454546 Combine like terms: -1.139087645 + 1.545454546 = 0.406366901 x = 0.406366901 Simplifying x = 0.406366901Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.684542191, 0.406366901}
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