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Simplifying 0 = -9.8x2 + 89x + 100 Reorder the terms: 0 = 100 + 89x + -9.8x2 Solving 0 = 100 + 89x + -9.8x2 Solving for variable 'x'. Combine like terms: 0 + -100 = -100 -100 + -89x + 9.8x2 = 100 + 89x + -9.8x2 + -100 + -89x + 9.8x2 Reorder the terms: -100 + -89x + 9.8x2 = 100 + -100 + 89x + -89x + -9.8x2 + 9.8x2 Combine like terms: 100 + -100 = 0 -100 + -89x + 9.8x2 = 0 + 89x + -89x + -9.8x2 + 9.8x2 -100 + -89x + 9.8x2 = 89x + -89x + -9.8x2 + 9.8x2 Combine like terms: 89x + -89x = 0 -100 + -89x + 9.8x2 = 0 + -9.8x2 + 9.8x2 -100 + -89x + 9.8x2 = -9.8x2 + 9.8x2 Combine like terms: -9.8x2 + 9.8x2 = 0.0 -100 + -89x + 9.8x2 = 0.0 Begin completing the square. Divide all terms by 9.8 the coefficient of the squared term: Divide each side by '9.8'. -10.20408163 + -9.081632653x + x2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + -9.081632653x + 10.20408163 + x2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + -9.081632653x + x2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + -9.081632653x + x2 = 0 + 10.20408163 -9.081632653x + x2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 -9.081632653x + x2 = 10.20408163 The x term is -9.081632653x. Take half its coefficient (-4.540816327). Square it (20.61901292) and add it to both sides. Add '20.61901292' to each side of the equation. -9.081632653x + 20.61901292 + x2 = 10.20408163 + 20.61901292 Reorder the terms: 20.61901292 + -9.081632653x + x2 = 10.20408163 + 20.61901292 Combine like terms: 10.20408163 + 20.61901292 = 30.82309455 20.61901292 + -9.081632653x + x2 = 30.82309455 Factor a perfect square on the left side: (x + -4.540816327)(x + -4.540816327) = 30.82309455 Calculate the square root of the right side: 5.551855055 Break this problem into two subproblems by setting (x + -4.540816327) equal to 5.551855055 and -5.551855055.Subproblem 1
x + -4.540816327 = 5.551855055 Simplifying x + -4.540816327 = 5.551855055 Reorder the terms: -4.540816327 + x = 5.551855055 Solving -4.540816327 + x = 5.551855055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.540816327' to each side of the equation. -4.540816327 + 4.540816327 + x = 5.551855055 + 4.540816327 Combine like terms: -4.540816327 + 4.540816327 = 0.000000000 0.000000000 + x = 5.551855055 + 4.540816327 x = 5.551855055 + 4.540816327 Combine like terms: 5.551855055 + 4.540816327 = 10.092671382 x = 10.092671382 Simplifying x = 10.092671382Subproblem 2
x + -4.540816327 = -5.551855055 Simplifying x + -4.540816327 = -5.551855055 Reorder the terms: -4.540816327 + x = -5.551855055 Solving -4.540816327 + x = -5.551855055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.540816327' to each side of the equation. -4.540816327 + 4.540816327 + x = -5.551855055 + 4.540816327 Combine like terms: -4.540816327 + 4.540816327 = 0.000000000 0.000000000 + x = -5.551855055 + 4.540816327 x = -5.551855055 + 4.540816327 Combine like terms: -5.551855055 + 4.540816327 = -1.011038728 x = -1.011038728 Simplifying x = -1.011038728Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.092671382, -1.011038728}
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