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Simplifying 0 = -4.9x2 + -2x + 50 Reorder the terms: 0 = 50 + -2x + -4.9x2 Solving 0 = 50 + -2x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -50 = -50 -50 + 2x + 4.9x2 = 50 + -2x + -4.9x2 + -50 + 2x + 4.9x2 Reorder the terms: -50 + 2x + 4.9x2 = 50 + -50 + -2x + 2x + -4.9x2 + 4.9x2 Combine like terms: 50 + -50 = 0 -50 + 2x + 4.9x2 = 0 + -2x + 2x + -4.9x2 + 4.9x2 -50 + 2x + 4.9x2 = -2x + 2x + -4.9x2 + 4.9x2 Combine like terms: -2x + 2x = 0 -50 + 2x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -50 + 2x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -50 + 2x + 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 + 0.4081632653x + x2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + 0.4081632653x + 10.20408163 + x2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + 0.4081632653x + x2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + 0.4081632653x + x2 = 0 + 10.20408163 0.4081632653x + x2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 0.4081632653x + x2 = 10.20408163 The x term is 0.4081632653x. Take half its coefficient (0.2040816327). Square it (0.04164931281) and add it to both sides. Add '0.04164931281' to each side of the equation. 0.4081632653x + 0.04164931281 + x2 = 10.20408163 + 0.04164931281 Reorder the terms: 0.04164931281 + 0.4081632653x + x2 = 10.20408163 + 0.04164931281 Combine like terms: 10.20408163 + 0.04164931281 = 10.24573094281 0.04164931281 + 0.4081632653x + x2 = 10.24573094281 Factor a perfect square on the left side: (x + 0.2040816327)(x + 0.2040816327) = 10.24573094281 Calculate the square root of the right side: 3.200895335 Break this problem into two subproblems by setting (x + 0.2040816327) equal to 3.200895335 and -3.200895335.Subproblem 1
x + 0.2040816327 = 3.200895335 Simplifying x + 0.2040816327 = 3.200895335 Reorder the terms: 0.2040816327 + x = 3.200895335 Solving 0.2040816327 + x = 3.200895335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2040816327' to each side of the equation. 0.2040816327 + -0.2040816327 + x = 3.200895335 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + x = 3.200895335 + -0.2040816327 x = 3.200895335 + -0.2040816327 Combine like terms: 3.200895335 + -0.2040816327 = 2.9968137023 x = 2.9968137023 Simplifying x = 2.9968137023Subproblem 2
x + 0.2040816327 = -3.200895335 Simplifying x + 0.2040816327 = -3.200895335 Reorder the terms: 0.2040816327 + x = -3.200895335 Solving 0.2040816327 + x = -3.200895335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2040816327' to each side of the equation. 0.2040816327 + -0.2040816327 + x = -3.200895335 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + x = -3.200895335 + -0.2040816327 x = -3.200895335 + -0.2040816327 Combine like terms: -3.200895335 + -0.2040816327 = -3.4049769677 x = -3.4049769677 Simplifying x = -3.4049769677Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9968137023, -3.4049769677}
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