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Simplifying 2 + -5(9X + -1(7X2 + -6X)) = 0 Reorder the terms: 2 + -5(9X + -1(-6X + 7X2)) = 0 2 + -5(9X + (-6X * -1 + 7X2 * -1)) = 0 2 + -5(9X + (6X + -7X2)) = 0 Combine like terms: 9X + 6X = 15X 2 + -5(15X + -7X2) = 0 2 + (15X * -5 + -7X2 * -5) = 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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