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Simplifying 0 = -4.9x2 + 50x + 200 Reorder the terms: 0 = 200 + 50x + -4.9x2 Solving 0 = 200 + 50x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -200 = -200 -200 + -50x + 4.9x2 = 200 + 50x + -4.9x2 + -200 + -50x + 4.9x2 Reorder the terms: -200 + -50x + 4.9x2 = 200 + -200 + 50x + -50x + -4.9x2 + 4.9x2 Combine like terms: 200 + -200 = 0 -200 + -50x + 4.9x2 = 0 + 50x + -50x + -4.9x2 + 4.9x2 -200 + -50x + 4.9x2 = 50x + -50x + -4.9x2 + 4.9x2 Combine like terms: 50x + -50x = 0 -200 + -50x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -200 + -50x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -200 + -50x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -40.81632653 + -10.20408163x + x2 = 0 Move the constant term to the right: Add '40.81632653' to each side of the equation. -40.81632653 + -10.20408163x + 40.81632653 + x2 = 0 + 40.81632653 Reorder the terms: -40.81632653 + 40.81632653 + -10.20408163x + x2 = 0 + 40.81632653 Combine like terms: -40.81632653 + 40.81632653 = 0.00000000 0.00000000 + -10.20408163x + x2 = 0 + 40.81632653 -10.20408163x + x2 = 0 + 40.81632653 Combine like terms: 0 + 40.81632653 = 40.81632653 -10.20408163x + x2 = 40.81632653 The x term is -10.20408163x. Take half its coefficient (-5.102040815). Square it (26.03082048) and add it to both sides. Add '26.03082048' to each side of the equation. -10.20408163x + 26.03082048 + x2 = 40.81632653 + 26.03082048 Reorder the terms: 26.03082048 + -10.20408163x + x2 = 40.81632653 + 26.03082048 Combine like terms: 40.81632653 + 26.03082048 = 66.84714701 26.03082048 + -10.20408163x + x2 = 66.84714701 Factor a perfect square on the left side: (x + -5.102040815)(x + -5.102040815) = 66.84714701 Calculate the square root of the right side: 8.176010458 Break this problem into two subproblems by setting (x + -5.102040815) equal to 8.176010458 and -8.176010458.Subproblem 1
x + -5.102040815 = 8.176010458 Simplifying x + -5.102040815 = 8.176010458 Reorder the terms: -5.102040815 + x = 8.176010458 Solving -5.102040815 + x = 8.176010458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.102040815' to each side of the equation. -5.102040815 + 5.102040815 + x = 8.176010458 + 5.102040815 Combine like terms: -5.102040815 + 5.102040815 = 0.000000000 0.000000000 + x = 8.176010458 + 5.102040815 x = 8.176010458 + 5.102040815 Combine like terms: 8.176010458 + 5.102040815 = 13.278051273 x = 13.278051273 Simplifying x = 13.278051273Subproblem 2
x + -5.102040815 = -8.176010458 Simplifying x + -5.102040815 = -8.176010458 Reorder the terms: -5.102040815 + x = -8.176010458 Solving -5.102040815 + x = -8.176010458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.102040815' to each side of the equation. -5.102040815 + 5.102040815 + x = -8.176010458 + 5.102040815 Combine like terms: -5.102040815 + 5.102040815 = 0.000000000 0.000000000 + x = -8.176010458 + 5.102040815 x = -8.176010458 + 5.102040815 Combine like terms: -8.176010458 + 5.102040815 = -3.073969643 x = -3.073969643 Simplifying x = -3.073969643Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.278051273, -3.073969643}
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