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Simplifying 576 + -16x2 = 4.9x2 + -9.8x Reorder the terms: 576 + -16x2 = -9.8x + 4.9x2 Solving 576 + -16x2 = -9.8x + 4.9x2 Solving for variable 'x'. Reorder the terms: 576 + 9.8x + -16x2 + -4.9x2 = -9.8x + 4.9x2 + 9.8x + -4.9x2 Combine like terms: -16x2 + -4.9x2 = -20.9x2 576 + 9.8x + -20.9x2 = -9.8x + 4.9x2 + 9.8x + -4.9x2 Reorder the terms: 576 + 9.8x + -20.9x2 = -9.8x + 9.8x + 4.9x2 + -4.9x2 Combine like terms: -9.8x + 9.8x = 0.0 576 + 9.8x + -20.9x2 = 0.0 + 4.9x2 + -4.9x2 576 + 9.8x + -20.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 576 + 9.8x + -20.9x2 = 0.0 Begin completing the square. Divide all terms by -20.9 the coefficient of the squared term: Divide each side by '-20.9'. -27.55980861 + -0.4688995215x + x2 = 0 Move the constant term to the right: Add '27.55980861' to each side of the equation. -27.55980861 + -0.4688995215x + 27.55980861 + x2 = 0 + 27.55980861 Reorder the terms: -27.55980861 + 27.55980861 + -0.4688995215x + x2 = 0 + 27.55980861 Combine like terms: -27.55980861 + 27.55980861 = 0.00000000 0.00000000 + -0.4688995215x + x2 = 0 + 27.55980861 -0.4688995215x + x2 = 0 + 27.55980861 Combine like terms: 0 + 27.55980861 = 27.55980861 -0.4688995215x + x2 = 27.55980861 The x term is -0.4688995215x. Take half its coefficient (-0.2344497608). Square it (0.05496669034) and add it to both sides. Add '0.05496669034' to each side of the equation. -0.4688995215x + 0.05496669034 + x2 = 27.55980861 + 0.05496669034 Reorder the terms: 0.05496669034 + -0.4688995215x + x2 = 27.55980861 + 0.05496669034 Combine like terms: 27.55980861 + 0.05496669034 = 27.61477530034 0.05496669034 + -0.4688995215x + x2 = 27.61477530034 Factor a perfect square on the left side: (x + -0.2344497608)(x + -0.2344497608) = 27.61477530034 Calculate the square root of the right side: 5.254976242 Break this problem into two subproblems by setting (x + -0.2344497608) equal to 5.254976242 and -5.254976242.Subproblem 1
x + -0.2344497608 = 5.254976242 Simplifying x + -0.2344497608 = 5.254976242 Reorder the terms: -0.2344497608 + x = 5.254976242 Solving -0.2344497608 + x = 5.254976242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2344497608' to each side of the equation. -0.2344497608 + 0.2344497608 + x = 5.254976242 + 0.2344497608 Combine like terms: -0.2344497608 + 0.2344497608 = 0.0000000000 0.0000000000 + x = 5.254976242 + 0.2344497608 x = 5.254976242 + 0.2344497608 Combine like terms: 5.254976242 + 0.2344497608 = 5.4894260028 x = 5.4894260028 Simplifying x = 5.4894260028Subproblem 2
x + -0.2344497608 = -5.254976242 Simplifying x + -0.2344497608 = -5.254976242 Reorder the terms: -0.2344497608 + x = -5.254976242 Solving -0.2344497608 + x = -5.254976242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2344497608' to each side of the equation. -0.2344497608 + 0.2344497608 + x = -5.254976242 + 0.2344497608 Combine like terms: -0.2344497608 + 0.2344497608 = 0.0000000000 0.0000000000 + x = -5.254976242 + 0.2344497608 x = -5.254976242 + 0.2344497608 Combine like terms: -5.254976242 + 0.2344497608 = -5.0205264812 x = -5.0205264812 Simplifying x = -5.0205264812Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.4894260028, -5.0205264812}
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