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Simplifying -4.9x2 + 349x + 101 = 0 Reorder the terms: 101 + 349x + -4.9x2 = 0 Solving 101 + 349x + -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'. -20.6122449 + -71.2244898x + x2 = 0 Move the constant term to the right: Add '20.6122449' to each side of the equation. -20.6122449 + -71.2244898x + 20.6122449 + x2 = 0 + 20.6122449 Reorder the terms: -20.6122449 + 20.6122449 + -71.2244898x + x2 = 0 + 20.6122449 Combine like terms: -20.6122449 + 20.6122449 = 0.0000000 0.0000000 + -71.2244898x + x2 = 0 + 20.6122449 -71.2244898x + x2 = 0 + 20.6122449 Combine like terms: 0 + 20.6122449 = 20.6122449 -71.2244898x + x2 = 20.6122449 The x term is -71.2244898x. Take half its coefficient (-35.6122449). Square it (1268.231987) and add it to both sides. Add '1268.231987' to each side of the equation. -71.2244898x + 1268.231987 + x2 = 20.6122449 + 1268.231987 Reorder the terms: 1268.231987 + -71.2244898x + x2 = 20.6122449 + 1268.231987 Combine like terms: 20.6122449 + 1268.231987 = 1288.8442319 1268.231987 + -71.2244898x + x2 = 1288.8442319 Factor a perfect square on the left side: (x + -35.6122449)(x + -35.6122449) = 1288.8442319 Calculate the square root of the right side: 35.900476764 Break this problem into two subproblems by setting (x + -35.6122449) equal to 35.900476764 and -35.900476764.Subproblem 1
x + -35.6122449 = 35.900476764 Simplifying x + -35.6122449 = 35.900476764 Reorder the terms: -35.6122449 + x = 35.900476764 Solving -35.6122449 + x = 35.900476764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35.6122449' to each side of the equation. -35.6122449 + 35.6122449 + x = 35.900476764 + 35.6122449 Combine like terms: -35.6122449 + 35.6122449 = 0.0000000 0.0000000 + x = 35.900476764 + 35.6122449 x = 35.900476764 + 35.6122449 Combine like terms: 35.900476764 + 35.6122449 = 71.512721664 x = 71.512721664 Simplifying x = 71.512721664Subproblem 2
x + -35.6122449 = -35.900476764 Simplifying x + -35.6122449 = -35.900476764 Reorder the terms: -35.6122449 + x = -35.900476764 Solving -35.6122449 + x = -35.900476764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35.6122449' to each side of the equation. -35.6122449 + 35.6122449 + x = -35.900476764 + 35.6122449 Combine like terms: -35.6122449 + 35.6122449 = 0.0000000 0.0000000 + x = -35.900476764 + 35.6122449 x = -35.900476764 + 35.6122449 Combine like terms: -35.900476764 + 35.6122449 = -0.288231864 x = -0.288231864 Simplifying x = -0.288231864Solution
The solution to the problem is based on the solutions from the subproblems. x = {71.512721664, -0.288231864}
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