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Simplifying -4.9x2 + 50x + 40 = 0 Reorder the terms: 40 + 50x + -4.9x2 = 0 Solving 40 + 50x + -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'. -8.163265306 + -10.20408163x + x2 = 0 Move the constant term to the right: Add '8.163265306' to each side of the equation. -8.163265306 + -10.20408163x + 8.163265306 + x2 = 0 + 8.163265306 Reorder the terms: -8.163265306 + 8.163265306 + -10.20408163x + x2 = 0 + 8.163265306 Combine like terms: -8.163265306 + 8.163265306 = 0.000000000 0.000000000 + -10.20408163x + x2 = 0 + 8.163265306 -10.20408163x + x2 = 0 + 8.163265306 Combine like terms: 0 + 8.163265306 = 8.163265306 -10.20408163x + x2 = 8.163265306 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 = 8.163265306 + 26.03082048 Reorder the terms: 26.03082048 + -10.20408163x + x2 = 8.163265306 + 26.03082048 Combine like terms: 8.163265306 + 26.03082048 = 34.194085786 26.03082048 + -10.20408163x + x2 = 34.194085786 Factor a perfect square on the left side: (x + -5.102040815)(x + -5.102040815) = 34.194085786 Calculate the square root of the right side: 5.84757093 Break this problem into two subproblems by setting (x + -5.102040815) equal to 5.84757093 and -5.84757093.Subproblem 1
x + -5.102040815 = 5.84757093 Simplifying x + -5.102040815 = 5.84757093 Reorder the terms: -5.102040815 + x = 5.84757093 Solving -5.102040815 + x = 5.84757093 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 = 5.84757093 + 5.102040815 Combine like terms: -5.102040815 + 5.102040815 = 0.000000000 0.000000000 + x = 5.84757093 + 5.102040815 x = 5.84757093 + 5.102040815 Combine like terms: 5.84757093 + 5.102040815 = 10.949611745 x = 10.949611745 Simplifying x = 10.949611745Subproblem 2
x + -5.102040815 = -5.84757093 Simplifying x + -5.102040815 = -5.84757093 Reorder the terms: -5.102040815 + x = -5.84757093 Solving -5.102040815 + x = -5.84757093 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 = -5.84757093 + 5.102040815 Combine like terms: -5.102040815 + 5.102040815 = 0.000000000 0.000000000 + x = -5.84757093 + 5.102040815 x = -5.84757093 + 5.102040815 Combine like terms: -5.84757093 + 5.102040815 = -0.745530115 x = -0.745530115 Simplifying x = -0.745530115Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.949611745, -0.745530115}
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