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Simplifying 26 = 0.0021x2 + -0.286x + 16.28 Reorder the terms: 26 = 16.28 + -0.286x + 0.0021x2 Solving 26 = 16.28 + -0.286x + 0.0021x2 Solving for variable 'x'. Combine like terms: 26 + -16.28 = 9.72 9.72 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2 Reorder the terms: 9.72 + 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 9.72 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 9.72 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: -0.286x + 0.286x = 0.000 9.72 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2 9.72 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2 Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000 9.72 + 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'. -4628.571429 + -136.1904762x + x2 = 0 Move the constant term to the right: Add '4628.571429' to each side of the equation. -4628.571429 + -136.1904762x + 4628.571429 + x2 = 0 + 4628.571429 Reorder the terms: -4628.571429 + 4628.571429 + -136.1904762x + x2 = 0 + 4628.571429 Combine like terms: -4628.571429 + 4628.571429 = 0.000000 0.000000 + -136.1904762x + x2 = 0 + 4628.571429 -136.1904762x + x2 = 0 + 4628.571429 Combine like terms: 0 + 4628.571429 = 4628.571429 -136.1904762x + x2 = 4628.571429 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 = 4628.571429 + 4636.961452 Reorder the terms: 4636.961452 + -136.1904762x + x2 = 4628.571429 + 4636.961452 Combine like terms: 4628.571429 + 4636.961452 = 9265.532881 4636.961452 + -136.1904762x + x2 = 9265.532881 Factor a perfect square on the left side: (x + -68.0952381)(x + -68.0952381) = 9265.532881 Calculate the square root of the right side: 96.25763804 Break this problem into two subproblems by setting (x + -68.0952381) equal to 96.25763804 and -96.25763804.Subproblem 1
x + -68.0952381 = 96.25763804 Simplifying x + -68.0952381 = 96.25763804 Reorder the terms: -68.0952381 + x = 96.25763804 Solving -68.0952381 + x = 96.25763804 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 = 96.25763804 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = 96.25763804 + 68.0952381 x = 96.25763804 + 68.0952381 Combine like terms: 96.25763804 + 68.0952381 = 164.35287614 x = 164.35287614 Simplifying x = 164.35287614Subproblem 2
x + -68.0952381 = -96.25763804 Simplifying x + -68.0952381 = -96.25763804 Reorder the terms: -68.0952381 + x = -96.25763804 Solving -68.0952381 + x = -96.25763804 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 = -96.25763804 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = -96.25763804 + 68.0952381 x = -96.25763804 + 68.0952381 Combine like terms: -96.25763804 + 68.0952381 = -28.16239994 x = -28.16239994 Simplifying x = -28.16239994Solution
The solution to the problem is based on the solutions from the subproblems. x = {164.35287614, -28.16239994}
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