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Simplifying 38 = 0.0021x2 + -0.286x + 16.28 Reorder the terms: 38 = 16.28 + -0.286x + 0.0021x2 Solving 38 = 16.28 + -0.286x + 0.0021x2 Solving for variable 'x'. Combine like terms: 38 + -16.28 = 21.72 21.72 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2 Reorder the terms: 21.72 + 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 21.72 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 21.72 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: -0.286x + 0.286x = 0.000 21.72 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2 21.72 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2 Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000 21.72 + 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'. -10342.85714 + -136.1904762x + x2 = 0 Move the constant term to the right: Add '10342.85714' to each side of the equation. -10342.85714 + -136.1904762x + 10342.85714 + x2 = 0 + 10342.85714 Reorder the terms: -10342.85714 + 10342.85714 + -136.1904762x + x2 = 0 + 10342.85714 Combine like terms: -10342.85714 + 10342.85714 = 0.00000 0.00000 + -136.1904762x + x2 = 0 + 10342.85714 -136.1904762x + x2 = 0 + 10342.85714 Combine like terms: 0 + 10342.85714 = 10342.85714 -136.1904762x + x2 = 10342.85714 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 = 10342.85714 + 4636.961452 Reorder the terms: 4636.961452 + -136.1904762x + x2 = 10342.85714 + 4636.961452 Combine like terms: 10342.85714 + 4636.961452 = 14979.818592 4636.961452 + -136.1904762x + x2 = 14979.818592 Factor a perfect square on the left side: (x + -68.0952381)(x + -68.0952381) = 14979.818592 Calculate the square root of the right side: 122.392069155 Break this problem into two subproblems by setting (x + -68.0952381) equal to 122.392069155 and -122.392069155.Subproblem 1
x + -68.0952381 = 122.392069155 Simplifying x + -68.0952381 = 122.392069155 Reorder the terms: -68.0952381 + x = 122.392069155 Solving -68.0952381 + x = 122.392069155 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 = 122.392069155 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = 122.392069155 + 68.0952381 x = 122.392069155 + 68.0952381 Combine like terms: 122.392069155 + 68.0952381 = 190.487307255 x = 190.487307255 Simplifying x = 190.487307255Subproblem 2
x + -68.0952381 = -122.392069155 Simplifying x + -68.0952381 = -122.392069155 Reorder the terms: -68.0952381 + x = -122.392069155 Solving -68.0952381 + x = -122.392069155 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 = -122.392069155 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = -122.392069155 + 68.0952381 x = -122.392069155 + 68.0952381 Combine like terms: -122.392069155 + 68.0952381 = -54.296831055 x = -54.296831055 Simplifying x = -54.296831055Solution
The solution to the problem is based on the solutions from the subproblems. x = {190.487307255, -54.296831055}
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