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Simplifying 6.55 = 0.0021x2 + -0.286x + 16.28 Reorder the terms: 6.55 = 16.28 + -0.286x + 0.0021x2 Solving 6.55 = 16.28 + -0.286x + 0.0021x2 Solving for variable 'x'. Combine like terms: 6.55 + -16.28 = -9.73 -9.73 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2 Reorder the terms: -9.73 + 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 -9.73 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 -9.73 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: -0.286x + 0.286x = 0.000 -9.73 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2 -9.73 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2 Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000 -9.73 + 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'. 4633.333333 + -136.1904762x + x2 = 0 Move the constant term to the right: Add '-4633.333333' to each side of the equation. 4633.333333 + -136.1904762x + -4633.333333 + x2 = 0 + -4633.333333 Reorder the terms: 4633.333333 + -4633.333333 + -136.1904762x + x2 = 0 + -4633.333333 Combine like terms: 4633.333333 + -4633.333333 = 0.000000 0.000000 + -136.1904762x + x2 = 0 + -4633.333333 -136.1904762x + x2 = 0 + -4633.333333 Combine like terms: 0 + -4633.333333 = -4633.333333 -136.1904762x + x2 = -4633.333333 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 = -4633.333333 + 4636.961452 Reorder the terms: 4636.961452 + -136.1904762x + x2 = -4633.333333 + 4636.961452 Combine like terms: -4633.333333 + 4636.961452 = 3.628119 4636.961452 + -136.1904762x + x2 = 3.628119 Factor a perfect square on the left side: (x + -68.0952381)(x + -68.0952381) = 3.628119 Calculate the square root of the right side: 1.90476219 Break this problem into two subproblems by setting (x + -68.0952381) equal to 1.90476219 and -1.90476219.Subproblem 1
x + -68.0952381 = 1.90476219 Simplifying x + -68.0952381 = 1.90476219 Reorder the terms: -68.0952381 + x = 1.90476219 Solving -68.0952381 + x = 1.90476219 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 = 1.90476219 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = 1.90476219 + 68.0952381 x = 1.90476219 + 68.0952381 Combine like terms: 1.90476219 + 68.0952381 = 70.00000029 x = 70.00000029 Simplifying x = 70.00000029Subproblem 2
x + -68.0952381 = -1.90476219 Simplifying x + -68.0952381 = -1.90476219 Reorder the terms: -68.0952381 + x = -1.90476219 Solving -68.0952381 + x = -1.90476219 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 = -1.90476219 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = -1.90476219 + 68.0952381 x = -1.90476219 + 68.0952381 Combine like terms: -1.90476219 + 68.0952381 = 66.19047591 x = 66.19047591 Simplifying x = 66.19047591Solution
The solution to the problem is based on the solutions from the subproblems. x = {70.00000029, 66.19047591}
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