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Simplifying 37 = 0.0021x2 + -0.286x + 16.28 Reorder the terms: 37 = 16.28 + -0.286x + 0.0021x2 Solving 37 = 16.28 + -0.286x + 0.0021x2 Solving for variable 'x'. Combine like terms: 37 + -16.28 = 20.72 20.72 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2 Reorder the terms: 20.72 + 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 20.72 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 20.72 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: -0.286x + 0.286x = 0.000 20.72 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2 20.72 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2 Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000 20.72 + 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'. -9866.666667 + -136.1904762x + x2 = 0 Move the constant term to the right: Add '9866.666667' to each side of the equation. -9866.666667 + -136.1904762x + 9866.666667 + x2 = 0 + 9866.666667 Reorder the terms: -9866.666667 + 9866.666667 + -136.1904762x + x2 = 0 + 9866.666667 Combine like terms: -9866.666667 + 9866.666667 = 0.000000 0.000000 + -136.1904762x + x2 = 0 + 9866.666667 -136.1904762x + x2 = 0 + 9866.666667 Combine like terms: 0 + 9866.666667 = 9866.666667 -136.1904762x + x2 = 9866.666667 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 = 9866.666667 + 4636.961452 Reorder the terms: 4636.961452 + -136.1904762x + x2 = 9866.666667 + 4636.961452 Combine like terms: 9866.666667 + 4636.961452 = 14503.628119 4636.961452 + -136.1904762x + x2 = 14503.628119 Factor a perfect square on the left side: (x + -68.0952381)(x + -68.0952381) = 14503.628119 Calculate the square root of the right side: 120.43100979 Break this problem into two subproblems by setting (x + -68.0952381) equal to 120.43100979 and -120.43100979.Subproblem 1
x + -68.0952381 = 120.43100979 Simplifying x + -68.0952381 = 120.43100979 Reorder the terms: -68.0952381 + x = 120.43100979 Solving -68.0952381 + x = 120.43100979 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 = 120.43100979 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = 120.43100979 + 68.0952381 x = 120.43100979 + 68.0952381 Combine like terms: 120.43100979 + 68.0952381 = 188.52624789 x = 188.52624789 Simplifying x = 188.52624789Subproblem 2
x + -68.0952381 = -120.43100979 Simplifying x + -68.0952381 = -120.43100979 Reorder the terms: -68.0952381 + x = -120.43100979 Solving -68.0952381 + x = -120.43100979 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 = -120.43100979 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = -120.43100979 + 68.0952381 x = -120.43100979 + 68.0952381 Combine like terms: -120.43100979 + 68.0952381 = -52.33577169 x = -52.33577169 Simplifying x = -52.33577169Solution
The solution to the problem is based on the solutions from the subproblems. x = {188.52624789, -52.33577169}
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