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Simplifying 27 = 0.0021x2 + -0.286x + 16.28 Reorder the terms: 27 = 16.28 + -0.286x + 0.0021x2 Solving 27 = 16.28 + -0.286x + 0.0021x2 Solving for variable 'x'. Combine like terms: 27 + -16.28 = 10.72 10.72 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2 Reorder the terms: 10.72 + 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 10.72 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 10.72 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: -0.286x + 0.286x = 0.000 10.72 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2 10.72 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2 Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000 10.72 + 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'. -5104.761905 + -136.1904762x + x2 = 0 Move the constant term to the right: Add '5104.761905' to each side of the equation. -5104.761905 + -136.1904762x + 5104.761905 + x2 = 0 + 5104.761905 Reorder the terms: -5104.761905 + 5104.761905 + -136.1904762x + x2 = 0 + 5104.761905 Combine like terms: -5104.761905 + 5104.761905 = 0.000000 0.000000 + -136.1904762x + x2 = 0 + 5104.761905 -136.1904762x + x2 = 0 + 5104.761905 Combine like terms: 0 + 5104.761905 = 5104.761905 -136.1904762x + x2 = 5104.761905 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 = 5104.761905 + 4636.961452 Reorder the terms: 4636.961452 + -136.1904762x + x2 = 5104.761905 + 4636.961452 Combine like terms: 5104.761905 + 4636.961452 = 9741.723357 4636.961452 + -136.1904762x + x2 = 9741.723357 Factor a perfect square on the left side: (x + -68.0952381)(x + -68.0952381) = 9741.723357 Calculate the square root of the right side: 98.700168982 Break this problem into two subproblems by setting (x + -68.0952381) equal to 98.700168982 and -98.700168982.Subproblem 1
x + -68.0952381 = 98.700168982 Simplifying x + -68.0952381 = 98.700168982 Reorder the terms: -68.0952381 + x = 98.700168982 Solving -68.0952381 + x = 98.700168982 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 = 98.700168982 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = 98.700168982 + 68.0952381 x = 98.700168982 + 68.0952381 Combine like terms: 98.700168982 + 68.0952381 = 166.795407082 x = 166.795407082 Simplifying x = 166.795407082Subproblem 2
x + -68.0952381 = -98.700168982 Simplifying x + -68.0952381 = -98.700168982 Reorder the terms: -68.0952381 + x = -98.700168982 Solving -68.0952381 + x = -98.700168982 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 = -98.700168982 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = -98.700168982 + 68.0952381 x = -98.700168982 + 68.0952381 Combine like terms: -98.700168982 + 68.0952381 = -30.604930882 x = -30.604930882 Simplifying x = -30.604930882Solution
The solution to the problem is based on the solutions from the subproblems. x = {166.795407082, -30.604930882}
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