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Simplifying 0 = -4.9x2 + 50x + -50 Reorder the terms: 0 = -50 + 50x + -4.9x2 Solving 0 = -50 + 50x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + 50 = 50 50 + -50x + 4.9x2 = -50 + 50x + -4.9x2 + 50 + -50x + 4.9x2 Reorder the terms: 50 + -50x + 4.9x2 = -50 + 50 + 50x + -50x + -4.9x2 + 4.9x2 Combine like terms: -50 + 50 = 0 50 + -50x + 4.9x2 = 0 + 50x + -50x + -4.9x2 + 4.9x2 50 + -50x + 4.9x2 = 50x + -50x + -4.9x2 + 4.9x2 Combine like terms: 50x + -50x = 0 50 + -50x + 4.9x2 = 0 + -4.9x2 + 4.9x2 50 + -50x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 50 + -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'. 10.20408163 + -10.20408163x + x2 = 0 Move the constant term to the right: Add '-10.20408163' to each side of the equation. 10.20408163 + -10.20408163x + -10.20408163 + x2 = 0 + -10.20408163 Reorder the terms: 10.20408163 + -10.20408163 + -10.20408163x + x2 = 0 + -10.20408163 Combine like terms: 10.20408163 + -10.20408163 = 0.00000000 0.00000000 + -10.20408163x + x2 = 0 + -10.20408163 -10.20408163x + x2 = 0 + -10.20408163 Combine like terms: 0 + -10.20408163 = -10.20408163 -10.20408163x + x2 = -10.20408163 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 = -10.20408163 + 26.03082048 Reorder the terms: 26.03082048 + -10.20408163x + x2 = -10.20408163 + 26.03082048 Combine like terms: -10.20408163 + 26.03082048 = 15.82673885 26.03082048 + -10.20408163x + x2 = 15.82673885 Factor a perfect square on the left side: (x + -5.102040815)(x + -5.102040815) = 15.82673885 Calculate the square root of the right side: 3.978283405 Break this problem into two subproblems by setting (x + -5.102040815) equal to 3.978283405 and -3.978283405.Subproblem 1
x + -5.102040815 = 3.978283405 Simplifying x + -5.102040815 = 3.978283405 Reorder the terms: -5.102040815 + x = 3.978283405 Solving -5.102040815 + x = 3.978283405 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 = 3.978283405 + 5.102040815 Combine like terms: -5.102040815 + 5.102040815 = 0.000000000 0.000000000 + x = 3.978283405 + 5.102040815 x = 3.978283405 + 5.102040815 Combine like terms: 3.978283405 + 5.102040815 = 9.08032422 x = 9.08032422 Simplifying x = 9.08032422Subproblem 2
x + -5.102040815 = -3.978283405 Simplifying x + -5.102040815 = -3.978283405 Reorder the terms: -5.102040815 + x = -3.978283405 Solving -5.102040815 + x = -3.978283405 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 = -3.978283405 + 5.102040815 Combine like terms: -5.102040815 + 5.102040815 = 0.000000000 0.000000000 + x = -3.978283405 + 5.102040815 x = -3.978283405 + 5.102040815 Combine like terms: -3.978283405 + 5.102040815 = 1.12375741 x = 1.12375741 Simplifying x = 1.12375741Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.08032422, 1.12375741}
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