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Simplifying -4.9x2 + 11x + 600 = 0 Reorder the terms: 600 + 11x + -4.9x2 = 0 Solving 600 + 11x + -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 + -2.244897959x + x2 = 0 Move the constant term to the right: Add '122.4489796' to each side of the equation. -122.4489796 + -2.244897959x + 122.4489796 + x2 = 0 + 122.4489796 Reorder the terms: -122.4489796 + 122.4489796 + -2.244897959x + x2 = 0 + 122.4489796 Combine like terms: -122.4489796 + 122.4489796 = 0.0000000 0.0000000 + -2.244897959x + x2 = 0 + 122.4489796 -2.244897959x + x2 = 0 + 122.4489796 Combine like terms: 0 + 122.4489796 = 122.4489796 -2.244897959x + x2 = 122.4489796 The x term is -2.244897959x. Take half its coefficient (-1.12244898). Square it (1.259891713) and add it to both sides. Add '1.259891713' to each side of the equation. -2.244897959x + 1.259891713 + x2 = 122.4489796 + 1.259891713 Reorder the terms: 1.259891713 + -2.244897959x + x2 = 122.4489796 + 1.259891713 Combine like terms: 122.4489796 + 1.259891713 = 123.708871313 1.259891713 + -2.244897959x + x2 = 123.708871313 Factor a perfect square on the left side: (x + -1.12244898)(x + -1.12244898) = 123.708871313 Calculate the square root of the right side: 11.12244898 Break this problem into two subproblems by setting (x + -1.12244898) equal to 11.12244898 and -11.12244898.Subproblem 1
x + -1.12244898 = 11.12244898 Simplifying x + -1.12244898 = 11.12244898 Reorder the terms: -1.12244898 + x = 11.12244898 Solving -1.12244898 + x = 11.12244898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + x = 11.12244898 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + x = 11.12244898 + 1.12244898 x = 11.12244898 + 1.12244898 Combine like terms: 11.12244898 + 1.12244898 = 12.24489796 x = 12.24489796 Simplifying x = 12.24489796Subproblem 2
x + -1.12244898 = -11.12244898 Simplifying x + -1.12244898 = -11.12244898 Reorder the terms: -1.12244898 + x = -11.12244898 Solving -1.12244898 + x = -11.12244898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + x = -11.12244898 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + x = -11.12244898 + 1.12244898 x = -11.12244898 + 1.12244898 Combine like terms: -11.12244898 + 1.12244898 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.24489796, -10}
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