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Simplifying 50 = 0.014x2 + -4.322x + 282.11 Reorder the terms: 50 = 282.11 + -4.322x + 0.014x2 Solving 50 = 282.11 + -4.322x + 0.014x2 Solving for variable 'x'. Combine like terms: 50 + -282.11 = -232.11 -232.11 + 4.322x + -0.014x2 = 282.11 + -4.322x + 0.014x2 + -282.11 + 4.322x + -0.014x2 Reorder the terms: -232.11 + 4.322x + -0.014x2 = 282.11 + -282.11 + -4.322x + 4.322x + 0.014x2 + -0.014x2 Combine like terms: 282.11 + -282.11 = 0.00 -232.11 + 4.322x + -0.014x2 = 0.00 + -4.322x + 4.322x + 0.014x2 + -0.014x2 -232.11 + 4.322x + -0.014x2 = -4.322x + 4.322x + 0.014x2 + -0.014x2 Combine like terms: -4.322x + 4.322x = 0.000 -232.11 + 4.322x + -0.014x2 = 0.000 + 0.014x2 + -0.014x2 -232.11 + 4.322x + -0.014x2 = 0.014x2 + -0.014x2 Combine like terms: 0.014x2 + -0.014x2 = 0.000 -232.11 + 4.322x + -0.014x2 = 0.000 Begin completing the square. Divide all terms by -0.014 the coefficient of the squared term: Divide each side by '-0.014'. 16579.28571 + -308.7142857x + x2 = 0 Move the constant term to the right: Add '-16579.28571' to each side of the equation. 16579.28571 + -308.7142857x + -16579.28571 + x2 = 0 + -16579.28571 Reorder the terms: 16579.28571 + -16579.28571 + -308.7142857x + x2 = 0 + -16579.28571 Combine like terms: 16579.28571 + -16579.28571 = 0.00000 0.00000 + -308.7142857x + x2 = 0 + -16579.28571 -308.7142857x + x2 = 0 + -16579.28571 Combine like terms: 0 + -16579.28571 = -16579.28571 -308.7142857x + x2 = -16579.28571 The x term is -308.7142857x. Take half its coefficient (-154.3571429). Square it (23826.12756) and add it to both sides. Add '23826.12756' to each side of the equation. -308.7142857x + 23826.12756 + x2 = -16579.28571 + 23826.12756 Reorder the terms: 23826.12756 + -308.7142857x + x2 = -16579.28571 + 23826.12756 Combine like terms: -16579.28571 + 23826.12756 = 7246.84185 23826.12756 + -308.7142857x + x2 = 7246.84185 Factor a perfect square on the left side: (x + -154.3571429)(x + -154.3571429) = 7246.84185 Calculate the square root of the right side: 85.128384514 Break this problem into two subproblems by setting (x + -154.3571429) equal to 85.128384514 and -85.128384514.Subproblem 1
x + -154.3571429 = 85.128384514 Simplifying x + -154.3571429 = 85.128384514 Reorder the terms: -154.3571429 + x = 85.128384514 Solving -154.3571429 + x = 85.128384514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '154.3571429' to each side of the equation. -154.3571429 + 154.3571429 + x = 85.128384514 + 154.3571429 Combine like terms: -154.3571429 + 154.3571429 = 0.0000000 0.0000000 + x = 85.128384514 + 154.3571429 x = 85.128384514 + 154.3571429 Combine like terms: 85.128384514 + 154.3571429 = 239.485527414 x = 239.485527414 Simplifying x = 239.485527414Subproblem 2
x + -154.3571429 = -85.128384514 Simplifying x + -154.3571429 = -85.128384514 Reorder the terms: -154.3571429 + x = -85.128384514 Solving -154.3571429 + x = -85.128384514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '154.3571429' to each side of the equation. -154.3571429 + 154.3571429 + x = -85.128384514 + 154.3571429 Combine like terms: -154.3571429 + 154.3571429 = 0.0000000 0.0000000 + x = -85.128384514 + 154.3571429 x = -85.128384514 + 154.3571429 Combine like terms: -85.128384514 + 154.3571429 = 69.228758386 x = 69.228758386 Simplifying x = 69.228758386Solution
The solution to the problem is based on the solutions from the subproblems. x = {239.485527414, 69.228758386}
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