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Simplifying 2 + -1(45x + -1(35x2 + -30x)) = 0 Reorder the terms: 2 + -1(45x + -1(-30x + 35x2)) = 0 2 + -1(45x + (-30x * -1 + 35x2 * -1)) = 0 2 + -1(45x + (30x + -35x2)) = 0 Combine like terms: 45x + 30x = 75x 2 + -1(75x + -35x2) = 0 2 + (75x * -1 + -35x2 * -1) = 0 2 + (-75x + 35x2) = 0 Solving 2 + -75x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. 0.05714285714 + -2.142857143x + x2 = 0 Move the constant term to the right: Add '-0.05714285714' to each side of the equation. 0.05714285714 + -2.142857143x + -0.05714285714 + x2 = 0 + -0.05714285714 Reorder the terms: 0.05714285714 + -0.05714285714 + -2.142857143x + x2 = 0 + -0.05714285714 Combine like terms: 0.05714285714 + -0.05714285714 = 0.00000000000 0.00000000000 + -2.142857143x + x2 = 0 + -0.05714285714 -2.142857143x + x2 = 0 + -0.05714285714 Combine like terms: 0 + -0.05714285714 = -0.05714285714 -2.142857143x + x2 = -0.05714285714 The x term is -2.142857143x. Take half its coefficient (-1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. -2.142857143x + 1.147959185 + x2 = -0.05714285714 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143x + x2 = -0.05714285714 + 1.147959185 Combine like terms: -0.05714285714 + 1.147959185 = 1.09081632786 1.147959185 + -2.142857143x + x2 = 1.09081632786 Factor a perfect square on the left side: (x + -1.071428572)(x + -1.071428572) = 1.09081632786 Calculate the square root of the right side: 1.044421528 Break this problem into two subproblems by setting (x + -1.071428572) equal to 1.044421528 and -1.044421528.Subproblem 1
x + -1.071428572 = 1.044421528 Simplifying x + -1.071428572 = 1.044421528 Reorder the terms: -1.071428572 + x = 1.044421528 Solving -1.071428572 + x = 1.044421528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + x = 1.044421528 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = 1.044421528 + 1.071428572 x = 1.044421528 + 1.071428572 Combine like terms: 1.044421528 + 1.071428572 = 2.1158501 x = 2.1158501 Simplifying x = 2.1158501Subproblem 2
x + -1.071428572 = -1.044421528 Simplifying x + -1.071428572 = -1.044421528 Reorder the terms: -1.071428572 + x = -1.044421528 Solving -1.071428572 + x = -1.044421528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + x = -1.044421528 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + x = -1.044421528 + 1.071428572 x = -1.044421528 + 1.071428572 Combine like terms: -1.044421528 + 1.071428572 = 0.027007044 x = 0.027007044 Simplifying x = 0.027007044Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1158501, 0.027007044}
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