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Simplifying 22 = 0.0021x2 + -0.286x + 16.28 Reorder the terms: 22 = 16.28 + -0.286x + 0.0021x2 Solving 22 = 16.28 + -0.286x + 0.0021x2 Solving for variable 'x'. Combine like terms: 22 + -16.28 = 5.72 5.72 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2 Reorder the terms: 5.72 + 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 5.72 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 5.72 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: -0.286x + 0.286x = 0.000 5.72 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2 5.72 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2 Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000 5.72 + 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'. -2723.809524 + -136.1904762x + x2 = 0 Move the constant term to the right: Add '2723.809524' to each side of the equation. -2723.809524 + -136.1904762x + 2723.809524 + x2 = 0 + 2723.809524 Reorder the terms: -2723.809524 + 2723.809524 + -136.1904762x + x2 = 0 + 2723.809524 Combine like terms: -2723.809524 + 2723.809524 = 0.000000 0.000000 + -136.1904762x + x2 = 0 + 2723.809524 -136.1904762x + x2 = 0 + 2723.809524 Combine like terms: 0 + 2723.809524 = 2723.809524 -136.1904762x + x2 = 2723.809524 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 = 2723.809524 + 4636.961452 Reorder the terms: 4636.961452 + -136.1904762x + x2 = 2723.809524 + 4636.961452 Combine like terms: 2723.809524 + 4636.961452 = 7360.770976 4636.961452 + -136.1904762x + x2 = 7360.770976 Factor a perfect square on the left side: (x + -68.0952381)(x + -68.0952381) = 7360.770976 Calculate the square root of the right side: 85.794935608 Break this problem into two subproblems by setting (x + -68.0952381) equal to 85.794935608 and -85.794935608.Subproblem 1
x + -68.0952381 = 85.794935608 Simplifying x + -68.0952381 = 85.794935608 Reorder the terms: -68.0952381 + x = 85.794935608 Solving -68.0952381 + x = 85.794935608 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 = 85.794935608 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = 85.794935608 + 68.0952381 x = 85.794935608 + 68.0952381 Combine like terms: 85.794935608 + 68.0952381 = 153.890173708 x = 153.890173708 Simplifying x = 153.890173708Subproblem 2
x + -68.0952381 = -85.794935608 Simplifying x + -68.0952381 = -85.794935608 Reorder the terms: -68.0952381 + x = -85.794935608 Solving -68.0952381 + x = -85.794935608 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 = -85.794935608 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = -85.794935608 + 68.0952381 x = -85.794935608 + 68.0952381 Combine like terms: -85.794935608 + 68.0952381 = -17.699697508 x = -17.699697508 Simplifying x = -17.699697508Solution
The solution to the problem is based on the solutions from the subproblems. x = {153.890173708, -17.699697508}
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