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Simplifying 17 = 0.0021x2 + -0.286x + 16.28 Reorder the terms: 17 = 16.28 + -0.286x + 0.0021x2 Solving 17 = 16.28 + -0.286x + 0.0021x2 Solving for variable 'x'. Combine like terms: 17 + -16.28 = 0.72 0.72 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2 Reorder the terms: 0.72 + 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 0.72 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 0.72 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: -0.286x + 0.286x = 0.000 0.72 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2 0.72 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2 Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000 0.72 + 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'. -342.8571429 + -136.1904762x + x2 = 0 Move the constant term to the right: Add '342.8571429' to each side of the equation. -342.8571429 + -136.1904762x + 342.8571429 + x2 = 0 + 342.8571429 Reorder the terms: -342.8571429 + 342.8571429 + -136.1904762x + x2 = 0 + 342.8571429 Combine like terms: -342.8571429 + 342.8571429 = 0.0000000 0.0000000 + -136.1904762x + x2 = 0 + 342.8571429 -136.1904762x + x2 = 0 + 342.8571429 Combine like terms: 0 + 342.8571429 = 342.8571429 -136.1904762x + x2 = 342.8571429 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 = 342.8571429 + 4636.961452 Reorder the terms: 4636.961452 + -136.1904762x + x2 = 342.8571429 + 4636.961452 Combine like terms: 342.8571429 + 4636.961452 = 4979.8185949 4636.961452 + -136.1904762x + x2 = 4979.8185949 Factor a perfect square on the left side: (x + -68.0952381)(x + -68.0952381) = 4979.8185949 Calculate the square root of the right side: 70.567829745 Break this problem into two subproblems by setting (x + -68.0952381) equal to 70.567829745 and -70.567829745.Subproblem 1
x + -68.0952381 = 70.567829745 Simplifying x + -68.0952381 = 70.567829745 Reorder the terms: -68.0952381 + x = 70.567829745 Solving -68.0952381 + x = 70.567829745 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 = 70.567829745 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = 70.567829745 + 68.0952381 x = 70.567829745 + 68.0952381 Combine like terms: 70.567829745 + 68.0952381 = 138.663067845 x = 138.663067845 Simplifying x = 138.663067845Subproblem 2
x + -68.0952381 = -70.567829745 Simplifying x + -68.0952381 = -70.567829745 Reorder the terms: -68.0952381 + x = -70.567829745 Solving -68.0952381 + x = -70.567829745 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 = -70.567829745 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = -70.567829745 + 68.0952381 x = -70.567829745 + 68.0952381 Combine like terms: -70.567829745 + 68.0952381 = -2.472591645 x = -2.472591645 Simplifying x = -2.472591645Solution
The solution to the problem is based on the solutions from the subproblems. x = {138.663067845, -2.472591645}
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