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Simplifying -4.9x2 + 100x + -297 = 0 Reorder the terms: -297 + 100x + -4.9x2 = 0 Solving -297 + 100x + -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'. 60.6122449 + -20.40816327x + x2 = 0 Move the constant term to the right: Add '-60.6122449' to each side of the equation. 60.6122449 + -20.40816327x + -60.6122449 + x2 = 0 + -60.6122449 Reorder the terms: 60.6122449 + -60.6122449 + -20.40816327x + x2 = 0 + -60.6122449 Combine like terms: 60.6122449 + -60.6122449 = 0.0000000 0.0000000 + -20.40816327x + x2 = 0 + -60.6122449 -20.40816327x + x2 = 0 + -60.6122449 Combine like terms: 0 + -60.6122449 = -60.6122449 -20.40816327x + x2 = -60.6122449 The x term is -20.40816327x. Take half its coefficient (-10.20408164). Square it (104.1232821) and add it to both sides. Add '104.1232821' to each side of the equation. -20.40816327x + 104.1232821 + x2 = -60.6122449 + 104.1232821 Reorder the terms: 104.1232821 + -20.40816327x + x2 = -60.6122449 + 104.1232821 Combine like terms: -60.6122449 + 104.1232821 = 43.5110372 104.1232821 + -20.40816327x + x2 = 43.5110372 Factor a perfect square on the left side: (x + -10.20408164)(x + -10.20408164) = 43.5110372 Calculate the square root of the right side: 6.596289654 Break this problem into two subproblems by setting (x + -10.20408164) equal to 6.596289654 and -6.596289654.Subproblem 1
x + -10.20408164 = 6.596289654 Simplifying x + -10.20408164 = 6.596289654 Reorder the terms: -10.20408164 + x = 6.596289654 Solving -10.20408164 + x = 6.596289654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.20408164' to each side of the equation. -10.20408164 + 10.20408164 + x = 6.596289654 + 10.20408164 Combine like terms: -10.20408164 + 10.20408164 = 0.00000000 0.00000000 + x = 6.596289654 + 10.20408164 x = 6.596289654 + 10.20408164 Combine like terms: 6.596289654 + 10.20408164 = 16.800371294 x = 16.800371294 Simplifying x = 16.800371294Subproblem 2
x + -10.20408164 = -6.596289654 Simplifying x + -10.20408164 = -6.596289654 Reorder the terms: -10.20408164 + x = -6.596289654 Solving -10.20408164 + x = -6.596289654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.20408164' to each side of the equation. -10.20408164 + 10.20408164 + x = -6.596289654 + 10.20408164 Combine like terms: -10.20408164 + 10.20408164 = 0.00000000 0.00000000 + x = -6.596289654 + 10.20408164 x = -6.596289654 + 10.20408164 Combine like terms: -6.596289654 + 10.20408164 = 3.607791986 x = 3.607791986 Simplifying x = 3.607791986Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.800371294, 3.607791986}
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