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Simplifying 39 = 0.0021x2 + -0.286x + 16.28 Reorder the terms: 39 = 16.28 + -0.286x + 0.0021x2 Solving 39 = 16.28 + -0.286x + 0.0021x2 Solving for variable 'x'. Combine like terms: 39 + -16.28 = 22.72 22.72 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2 Reorder the terms: 22.72 + 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 22.72 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 22.72 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: -0.286x + 0.286x = 0.000 22.72 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2 22.72 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2 Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000 22.72 + 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'. -10819.04762 + -136.1904762x + x2 = 0 Move the constant term to the right: Add '10819.04762' to each side of the equation. -10819.04762 + -136.1904762x + 10819.04762 + x2 = 0 + 10819.04762 Reorder the terms: -10819.04762 + 10819.04762 + -136.1904762x + x2 = 0 + 10819.04762 Combine like terms: -10819.04762 + 10819.04762 = 0.00000 0.00000 + -136.1904762x + x2 = 0 + 10819.04762 -136.1904762x + x2 = 0 + 10819.04762 Combine like terms: 0 + 10819.04762 = 10819.04762 -136.1904762x + x2 = 10819.04762 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 = 10819.04762 + 4636.961452 Reorder the terms: 4636.961452 + -136.1904762x + x2 = 10819.04762 + 4636.961452 Combine like terms: 10819.04762 + 4636.961452 = 15456.009072 4636.961452 + -136.1904762x + x2 = 15456.009072 Factor a perfect square on the left side: (x + -68.0952381)(x + -68.0952381) = 15456.009072 Calculate the square root of the right side: 124.322198629 Break this problem into two subproblems by setting (x + -68.0952381) equal to 124.322198629 and -124.322198629.Subproblem 1
x + -68.0952381 = 124.322198629 Simplifying x + -68.0952381 = 124.322198629 Reorder the terms: -68.0952381 + x = 124.322198629 Solving -68.0952381 + x = 124.322198629 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 = 124.322198629 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = 124.322198629 + 68.0952381 x = 124.322198629 + 68.0952381 Combine like terms: 124.322198629 + 68.0952381 = 192.417436729 x = 192.417436729 Simplifying x = 192.417436729Subproblem 2
x + -68.0952381 = -124.322198629 Simplifying x + -68.0952381 = -124.322198629 Reorder the terms: -68.0952381 + x = -124.322198629 Solving -68.0952381 + x = -124.322198629 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 = -124.322198629 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = -124.322198629 + 68.0952381 x = -124.322198629 + 68.0952381 Combine like terms: -124.322198629 + 68.0952381 = -56.226960529 x = -56.226960529 Simplifying x = -56.226960529Solution
The solution to the problem is based on the solutions from the subproblems. x = {192.417436729, -56.226960529}
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