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Simplifying -4.9x2 + -7x + 600 = 0 Reorder the terms: 600 + -7x + -4.9x2 = 0 Solving 600 + -7x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -122.4489796 + 1.428571429x + x2 = 0 Move the constant term to the right: Add '122.4489796' to each side of the equation. -122.4489796 + 1.428571429x + 122.4489796 + x2 = 0 + 122.4489796 Reorder the terms: -122.4489796 + 122.4489796 + 1.428571429x + x2 = 0 + 122.4489796 Combine like terms: -122.4489796 + 122.4489796 = 0.0000000 0.0000000 + 1.428571429x + x2 = 0 + 122.4489796 1.428571429x + x2 = 0 + 122.4489796 Combine like terms: 0 + 122.4489796 = 122.4489796 1.428571429x + x2 = 122.4489796 The x term is 1.428571429x. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429x + 0.5102040819 + x2 = 122.4489796 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429x + x2 = 122.4489796 + 0.5102040819 Combine like terms: 122.4489796 + 0.5102040819 = 122.9591836819 0.5102040819 + 1.428571429x + x2 = 122.9591836819 Factor a perfect square on the left side: (x + 0.7142857145)(x + 0.7142857145) = 122.9591836819 Calculate the square root of the right side: 11.088696212 Break this problem into two subproblems by setting (x + 0.7142857145) equal to 11.088696212 and -11.088696212.Subproblem 1
x + 0.7142857145 = 11.088696212 Simplifying x + 0.7142857145 = 11.088696212 Reorder the terms: 0.7142857145 + x = 11.088696212 Solving 0.7142857145 + x = 11.088696212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = 11.088696212 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 11.088696212 + -0.7142857145 x = 11.088696212 + -0.7142857145 Combine like terms: 11.088696212 + -0.7142857145 = 10.3744104975 x = 10.3744104975 Simplifying x = 10.3744104975Subproblem 2
x + 0.7142857145 = -11.088696212 Simplifying x + 0.7142857145 = -11.088696212 Reorder the terms: 0.7142857145 + x = -11.088696212 Solving 0.7142857145 + x = -11.088696212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = -11.088696212 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -11.088696212 + -0.7142857145 x = -11.088696212 + -0.7142857145 Combine like terms: -11.088696212 + -0.7142857145 = -11.8029819265 x = -11.8029819265 Simplifying x = -11.8029819265Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.3744104975, -11.8029819265}
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