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Simplifying -4.9x2 + 14x + 600 = 0 Reorder the terms: 600 + 14x + -4.9x2 = 0 Solving 600 + 14x + -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 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '122.4489796' to each side of the equation. -122.4489796 + -2.857142857x + 122.4489796 + x2 = 0 + 122.4489796 Reorder the terms: -122.4489796 + 122.4489796 + -2.857142857x + x2 = 0 + 122.4489796 Combine like terms: -122.4489796 + 122.4489796 = 0.0000000 0.0000000 + -2.857142857x + x2 = 0 + 122.4489796 -2.857142857x + x2 = 0 + 122.4489796 Combine like terms: 0 + 122.4489796 = 122.4489796 -2.857142857x + x2 = 122.4489796 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = 122.4489796 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = 122.4489796 + 2.040816328 Combine like terms: 122.4489796 + 2.040816328 = 124.489795928 2.040816328 + -2.857142857x + x2 = 124.489795928 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 124.489795928 Calculate the square root of the right side: 11.157499537 Break this problem into two subproblems by setting (x + -1.428571429) equal to 11.157499537 and -11.157499537.Subproblem 1
x + -1.428571429 = 11.157499537 Simplifying x + -1.428571429 = 11.157499537 Reorder the terms: -1.428571429 + x = 11.157499537 Solving -1.428571429 + x = 11.157499537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 11.157499537 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 11.157499537 + 1.428571429 x = 11.157499537 + 1.428571429 Combine like terms: 11.157499537 + 1.428571429 = 12.586070966 x = 12.586070966 Simplifying x = 12.586070966Subproblem 2
x + -1.428571429 = -11.157499537 Simplifying x + -1.428571429 = -11.157499537 Reorder the terms: -1.428571429 + x = -11.157499537 Solving -1.428571429 + x = -11.157499537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -11.157499537 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -11.157499537 + 1.428571429 x = -11.157499537 + 1.428571429 Combine like terms: -11.157499537 + 1.428571429 = -9.728928108 x = -9.728928108 Simplifying x = -9.728928108Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.586070966, -9.728928108}
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