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Simplifying 1900 = 0.0021x2 + -0.286x + 16.28 Reorder the terms: 1900 = 16.28 + -0.286x + 0.0021x2 Solving 1900 = 16.28 + -0.286x + 0.0021x2 Solving for variable 'x'. Combine like terms: 1900 + -16.28 = 1883.72 1883.72 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2 Reorder the terms: 1883.72 + 0.286x + -0.0021x2 = 16.28 + -16.28 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: 16.28 + -16.28 = 0.00 1883.72 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 1883.72 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: -0.286x + 0.286x = 0.000 1883.72 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2 1883.72 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2 Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000 1883.72 + 0.286x + -0.0021x2 = 0.0000 Begin completing the square. Divide all terms by -0.0021 the coefficient of the squared term: Divide each side by '-0.0021'. -897009.5238 + -136.1904762x + x2 = 0 Move the constant term to the right: Add '897009.5238' to each side of the equation. -897009.5238 + -136.1904762x + 897009.5238 + x2 = 0 + 897009.5238 Reorder the terms: -897009.5238 + 897009.5238 + -136.1904762x + x2 = 0 + 897009.5238 Combine like terms: -897009.5238 + 897009.5238 = 0.0000 0.0000 + -136.1904762x + x2 = 0 + 897009.5238 -136.1904762x + x2 = 0 + 897009.5238 Combine like terms: 0 + 897009.5238 = 897009.5238 -136.1904762x + x2 = 897009.5238 The x term is -136.1904762x. Take half its coefficient (-68.0952381). Square it (4636.961452) and add it to both sides. Add '4636.961452' to each side of the equation. -136.1904762x + 4636.961452 + x2 = 897009.5238 + 4636.961452 Reorder the terms: 4636.961452 + -136.1904762x + x2 = 897009.5238 + 4636.961452 Combine like terms: 897009.5238 + 4636.961452 = 901646.485252 4636.961452 + -136.1904762x + x2 = 901646.485252 Factor a perfect square on the left side: (x + -68.0952381)(x + -68.0952381) = 901646.485252 Calculate the square root of the right side: 949.550675452 Break this problem into two subproblems by setting (x + -68.0952381) equal to 949.550675452 and -949.550675452.Subproblem 1
x + -68.0952381 = 949.550675452 Simplifying x + -68.0952381 = 949.550675452 Reorder the terms: -68.0952381 + x = 949.550675452 Solving -68.0952381 + x = 949.550675452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '68.0952381' to each side of the equation. -68.0952381 + 68.0952381 + x = 949.550675452 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = 949.550675452 + 68.0952381 x = 949.550675452 + 68.0952381 Combine like terms: 949.550675452 + 68.0952381 = 1017.645913552 x = 1017.645913552 Simplifying x = 1017.645913552Subproblem 2
x + -68.0952381 = -949.550675452 Simplifying x + -68.0952381 = -949.550675452 Reorder the terms: -68.0952381 + x = -949.550675452 Solving -68.0952381 + x = -949.550675452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '68.0952381' to each side of the equation. -68.0952381 + 68.0952381 + x = -949.550675452 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = -949.550675452 + 68.0952381 x = -949.550675452 + 68.0952381 Combine like terms: -949.550675452 + 68.0952381 = -881.455437352 x = -881.455437352 Simplifying x = -881.455437352Solution
The solution to the problem is based on the solutions from the subproblems. x = {1017.645913552, -881.455437352}
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