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Simplifying 7x2 + -2800x + 4300 = 0 Reorder the terms: 4300 + -2800x + 7x2 = 0 Solving 4300 + -2800x + 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'. 614.2857143 + -400x + x2 = 0 Move the constant term to the right: Add '-614.2857143' to each side of the equation. 614.2857143 + -400x + -614.2857143 + x2 = 0 + -614.2857143 Reorder the terms: 614.2857143 + -614.2857143 + -400x + x2 = 0 + -614.2857143 Combine like terms: 614.2857143 + -614.2857143 = 0.0000000 0.0000000 + -400x + x2 = 0 + -614.2857143 -400x + x2 = 0 + -614.2857143 Combine like terms: 0 + -614.2857143 = -614.2857143 -400x + x2 = -614.2857143 The x term is -400x. Take half its coefficient (-200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. -400x + 40000 + x2 = -614.2857143 + 40000 Reorder the terms: 40000 + -400x + x2 = -614.2857143 + 40000 Combine like terms: -614.2857143 + 40000 = 39385.7142857 40000 + -400x + x2 = 39385.7142857 Factor a perfect square on the left side: (x + -200)(x + -200) = 39385.7142857 Calculate the square root of the right side: 198.458343956 Break this problem into two subproblems by setting (x + -200) equal to 198.458343956 and -198.458343956.Subproblem 1
x + -200 = 198.458343956 Simplifying x + -200 = 198.458343956 Reorder the terms: -200 + x = 198.458343956 Solving -200 + x = 198.458343956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x = 198.458343956 + 200 Combine like terms: -200 + 200 = 0 0 + x = 198.458343956 + 200 x = 198.458343956 + 200 Combine like terms: 198.458343956 + 200 = 398.458343956 x = 398.458343956 Simplifying x = 398.458343956Subproblem 2
x + -200 = -198.458343956 Simplifying x + -200 = -198.458343956 Reorder the terms: -200 + x = -198.458343956 Solving -200 + x = -198.458343956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x = -198.458343956 + 200 Combine like terms: -200 + 200 = 0 0 + x = -198.458343956 + 200 x = -198.458343956 + 200 Combine like terms: -198.458343956 + 200 = 1.541656044 x = 1.541656044 Simplifying x = 1.541656044Solution
The solution to the problem is based on the solutions from the subproblems. x = {398.458343956, 1.541656044}
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