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Simplifying 40 = 0.0021x2 + -0.286x + 16.28 Reorder the terms: 40 = 16.28 + -0.286x + 0.0021x2 Solving 40 = 16.28 + -0.286x + 0.0021x2 Solving for variable 'x'. Combine like terms: 40 + -16.28 = 23.72 23.72 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2 Reorder the terms: 23.72 + 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 23.72 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 23.72 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: -0.286x + 0.286x = 0.000 23.72 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2 23.72 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2 Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000 23.72 + 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'. -11295.2381 + -136.1904762x + x2 = 0 Move the constant term to the right: Add '11295.2381' to each side of the equation. -11295.2381 + -136.1904762x + 11295.2381 + x2 = 0 + 11295.2381 Reorder the terms: -11295.2381 + 11295.2381 + -136.1904762x + x2 = 0 + 11295.2381 Combine like terms: -11295.2381 + 11295.2381 = 0.0000 0.0000 + -136.1904762x + x2 = 0 + 11295.2381 -136.1904762x + x2 = 0 + 11295.2381 Combine like terms: 0 + 11295.2381 = 11295.2381 -136.1904762x + x2 = 11295.2381 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 = 11295.2381 + 4636.961452 Reorder the terms: 4636.961452 + -136.1904762x + x2 = 11295.2381 + 4636.961452 Combine like terms: 11295.2381 + 4636.961452 = 15932.199552 4636.961452 + -136.1904762x + x2 = 15932.199552 Factor a perfect square on the left side: (x + -68.0952381)(x + -68.0952381) = 15932.199552 Calculate the square root of the right side: 126.222817082 Break this problem into two subproblems by setting (x + -68.0952381) equal to 126.222817082 and -126.222817082.Subproblem 1
x + -68.0952381 = 126.222817082 Simplifying x + -68.0952381 = 126.222817082 Reorder the terms: -68.0952381 + x = 126.222817082 Solving -68.0952381 + x = 126.222817082 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 = 126.222817082 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = 126.222817082 + 68.0952381 x = 126.222817082 + 68.0952381 Combine like terms: 126.222817082 + 68.0952381 = 194.318055182 x = 194.318055182 Simplifying x = 194.318055182Subproblem 2
x + -68.0952381 = -126.222817082 Simplifying x + -68.0952381 = -126.222817082 Reorder the terms: -68.0952381 + x = -126.222817082 Solving -68.0952381 + x = -126.222817082 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 = -126.222817082 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = -126.222817082 + 68.0952381 x = -126.222817082 + 68.0952381 Combine like terms: -126.222817082 + 68.0952381 = -58.127578982 x = -58.127578982 Simplifying x = -58.127578982Solution
The solution to the problem is based on the solutions from the subproblems. x = {194.318055182, -58.127578982}
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