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Simplifying 7x2 + -128x + 350 = 0 Reorder the terms: 350 + -128x + 7x2 = 0 Solving 350 + -128x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 50 + -18.28571429x + x2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -18.28571429x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -18.28571429x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -18.28571429x + x2 = 0 + -50 -18.28571429x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -18.28571429x + x2 = -50 The x term is -18.28571429x. Take half its coefficient (-9.142857145). Square it (83.59183677) and add it to both sides. Add '83.59183677' to each side of the equation. -18.28571429x + 83.59183677 + x2 = -50 + 83.59183677 Reorder the terms: 83.59183677 + -18.28571429x + x2 = -50 + 83.59183677 Combine like terms: -50 + 83.59183677 = 33.59183677 83.59183677 + -18.28571429x + x2 = 33.59183677 Factor a perfect square on the left side: (x + -9.142857145)(x + -9.142857145) = 33.59183677 Calculate the square root of the right side: 5.79584651 Break this problem into two subproblems by setting (x + -9.142857145) equal to 5.79584651 and -5.79584651.Subproblem 1
x + -9.142857145 = 5.79584651 Simplifying x + -9.142857145 = 5.79584651 Reorder the terms: -9.142857145 + x = 5.79584651 Solving -9.142857145 + x = 5.79584651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.142857145' to each side of the equation. -9.142857145 + 9.142857145 + x = 5.79584651 + 9.142857145 Combine like terms: -9.142857145 + 9.142857145 = 0.000000000 0.000000000 + x = 5.79584651 + 9.142857145 x = 5.79584651 + 9.142857145 Combine like terms: 5.79584651 + 9.142857145 = 14.938703655 x = 14.938703655 Simplifying x = 14.938703655Subproblem 2
x + -9.142857145 = -5.79584651 Simplifying x + -9.142857145 = -5.79584651 Reorder the terms: -9.142857145 + x = -5.79584651 Solving -9.142857145 + x = -5.79584651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.142857145' to each side of the equation. -9.142857145 + 9.142857145 + x = -5.79584651 + 9.142857145 Combine like terms: -9.142857145 + 9.142857145 = 0.000000000 0.000000000 + x = -5.79584651 + 9.142857145 x = -5.79584651 + 9.142857145 Combine like terms: -5.79584651 + 9.142857145 = 3.347010635 x = 3.347010635 Simplifying x = 3.347010635Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.938703655, 3.347010635}
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