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Simplifying (0.49x2) + -7x + -4000 = 0 Reorder the terms: -4000 + -7x + (0.49x2) = 0 Solving -4000 + -7x + (0.49x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.49 the coefficient of the squared term: Divide each side by '0.49'. -8163.265306 + -14.28571429x + x2 = 0 Move the constant term to the right: Add '8163.265306' to each side of the equation. -8163.265306 + -14.28571429x + 8163.265306 + x2 = 0 + 8163.265306 Reorder the terms: -8163.265306 + 8163.265306 + -14.28571429x + x2 = 0 + 8163.265306 Combine like terms: -8163.265306 + 8163.265306 = 0.000000 0.000000 + -14.28571429x + x2 = 0 + 8163.265306 -14.28571429x + x2 = 0 + 8163.265306 Combine like terms: 0 + 8163.265306 = 8163.265306 -14.28571429x + x2 = 8163.265306 The x term is -14.28571429x. Take half its coefficient (-7.142857145). Square it (51.02040819) and add it to both sides. Add '51.02040819' to each side of the equation. -14.28571429x + 51.02040819 + x2 = 8163.265306 + 51.02040819 Reorder the terms: 51.02040819 + -14.28571429x + x2 = 8163.265306 + 51.02040819 Combine like terms: 8163.265306 + 51.02040819 = 8214.28571419 51.02040819 + -14.28571429x + x2 = 8214.28571419 Factor a perfect square on the left side: ((x) + -7.142857145)((x) + -7.142857145) = 8214.28571419 Calculate the square root of the right side: 90.632696717 Break this problem into two subproblems by setting ((x) + -7.142857145) equal to 90.632696717 and -90.632696717.Subproblem 1
(x) + -7.142857145 = 90.632696717 Simplifying (x) + -7.142857145 = 90.632696717 x + -7.142857145 = 90.632696717 Reorder the terms: -7.142857145 + x = 90.632696717 Solving -7.142857145 + x = 90.632696717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.142857145' to each side of the equation. -7.142857145 + 7.142857145 + x = 90.632696717 + 7.142857145 Combine like terms: -7.142857145 + 7.142857145 = 0.000000000 0.000000000 + x = 90.632696717 + 7.142857145 x = 90.632696717 + 7.142857145 Combine like terms: 90.632696717 + 7.142857145 = 97.775553862 x = 97.775553862 Simplifying x = 97.775553862Subproblem 2
(x) + -7.142857145 = -90.632696717 Simplifying (x) + -7.142857145 = -90.632696717 x + -7.142857145 = -90.632696717 Reorder the terms: -7.142857145 + x = -90.632696717 Solving -7.142857145 + x = -90.632696717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.142857145' to each side of the equation. -7.142857145 + 7.142857145 + x = -90.632696717 + 7.142857145 Combine like terms: -7.142857145 + 7.142857145 = 0.000000000 0.000000000 + x = -90.632696717 + 7.142857145 x = -90.632696717 + 7.142857145 Combine like terms: -90.632696717 + 7.142857145 = -83.489839572 x = -83.489839572 Simplifying x = -83.489839572Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.775553862, -83.489839572}
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