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Simplifying -2.6x(x + -2) + 3x = 1.2 Reorder the terms: -2.6x(-2 + x) + 3x = 1.2 (-2 * -2.6x + x * -2.6x) + 3x = 1.2 (5.2x + -2.6x2) + 3x = 1.2 Reorder the terms: 5.2x + 3x + -2.6x2 = 1.2 Combine like terms: 5.2x + 3x = 8.2x 8.2x + -2.6x2 = 1.2 Solving 8.2x + -2.6x2 = 1.2 Solving for variable 'x'. Reorder the terms: -1.2 + 8.2x + -2.6x2 = 1.2 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 -1.2 + 8.2x + -2.6x2 = 0.0 Begin completing the square. Divide all terms by -2.6 the coefficient of the squared term: Divide each side by '-2.6'. 0.4615384615 + -3.153846154x + x2 = 0 Move the constant term to the right: Add '-0.4615384615' to each side of the equation. 0.4615384615 + -3.153846154x + -0.4615384615 + x2 = 0 + -0.4615384615 Reorder the terms: 0.4615384615 + -0.4615384615 + -3.153846154x + x2 = 0 + -0.4615384615 Combine like terms: 0.4615384615 + -0.4615384615 = 0.0000000000 0.0000000000 + -3.153846154x + x2 = 0 + -0.4615384615 -3.153846154x + x2 = 0 + -0.4615384615 Combine like terms: 0 + -0.4615384615 = -0.4615384615 -3.153846154x + x2 = -0.4615384615 The x term is -3.153846154x. Take half its coefficient (-1.576923077). Square it (2.486686391) and add it to both sides. Add '2.486686391' to each side of the equation. -3.153846154x + 2.486686391 + x2 = -0.4615384615 + 2.486686391 Reorder the terms: 2.486686391 + -3.153846154x + x2 = -0.4615384615 + 2.486686391 Combine like terms: -0.4615384615 + 2.486686391 = 2.0251479295 2.486686391 + -3.153846154x + x2 = 2.0251479295 Factor a perfect square on the left side: (x + -1.576923077)(x + -1.576923077) = 2.0251479295 Calculate the square root of the right side: 1.423076923 Break this problem into two subproblems by setting (x + -1.576923077) equal to 1.423076923 and -1.423076923.Subproblem 1
x + -1.576923077 = 1.423076923 Simplifying x + -1.576923077 = 1.423076923 Reorder the terms: -1.576923077 + x = 1.423076923 Solving -1.576923077 + x = 1.423076923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.576923077' to each side of the equation. -1.576923077 + 1.576923077 + x = 1.423076923 + 1.576923077 Combine like terms: -1.576923077 + 1.576923077 = 0.000000000 0.000000000 + x = 1.423076923 + 1.576923077 x = 1.423076923 + 1.576923077 Combine like terms: 1.423076923 + 1.576923077 = 3 x = 3 Simplifying x = 3Subproblem 2
x + -1.576923077 = -1.423076923 Simplifying x + -1.576923077 = -1.423076923 Reorder the terms: -1.576923077 + x = -1.423076923 Solving -1.576923077 + x = -1.423076923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.576923077' to each side of the equation. -1.576923077 + 1.576923077 + x = -1.423076923 + 1.576923077 Combine like terms: -1.576923077 + 1.576923077 = 0.000000000 0.000000000 + x = -1.423076923 + 1.576923077 x = -1.423076923 + 1.576923077 Combine like terms: -1.423076923 + 1.576923077 = 0.153846154 x = 0.153846154 Simplifying x = 0.153846154Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, 0.153846154}
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