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Simplifying 34 = 0.0021x2 + -0.286x + 16.28 Reorder the terms: 34 = 16.28 + -0.286x + 0.0021x2 Solving 34 = 16.28 + -0.286x + 0.0021x2 Solving for variable 'x'. Combine like terms: 34 + -16.28 = 17.72 17.72 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2 Reorder the terms: 17.72 + 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 17.72 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2 17.72 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2 Combine like terms: -0.286x + 0.286x = 0.000 17.72 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2 17.72 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2 Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000 17.72 + 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'. -8438.095238 + -136.1904762x + x2 = 0 Move the constant term to the right: Add '8438.095238' to each side of the equation. -8438.095238 + -136.1904762x + 8438.095238 + x2 = 0 + 8438.095238 Reorder the terms: -8438.095238 + 8438.095238 + -136.1904762x + x2 = 0 + 8438.095238 Combine like terms: -8438.095238 + 8438.095238 = 0.000000 0.000000 + -136.1904762x + x2 = 0 + 8438.095238 -136.1904762x + x2 = 0 + 8438.095238 Combine like terms: 0 + 8438.095238 = 8438.095238 -136.1904762x + x2 = 8438.095238 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 = 8438.095238 + 4636.961452 Reorder the terms: 4636.961452 + -136.1904762x + x2 = 8438.095238 + 4636.961452 Combine like terms: 8438.095238 + 4636.961452 = 13075.05669 4636.961452 + -136.1904762x + x2 = 13075.05669 Factor a perfect square on the left side: (x + -68.0952381)(x + -68.0952381) = 13075.05669 Calculate the square root of the right side: 114.346214148 Break this problem into two subproblems by setting (x + -68.0952381) equal to 114.346214148 and -114.346214148.Subproblem 1
x + -68.0952381 = 114.346214148 Simplifying x + -68.0952381 = 114.346214148 Reorder the terms: -68.0952381 + x = 114.346214148 Solving -68.0952381 + x = 114.346214148 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 = 114.346214148 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = 114.346214148 + 68.0952381 x = 114.346214148 + 68.0952381 Combine like terms: 114.346214148 + 68.0952381 = 182.441452248 x = 182.441452248 Simplifying x = 182.441452248Subproblem 2
x + -68.0952381 = -114.346214148 Simplifying x + -68.0952381 = -114.346214148 Reorder the terms: -68.0952381 + x = -114.346214148 Solving -68.0952381 + x = -114.346214148 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 = -114.346214148 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = -114.346214148 + 68.0952381 x = -114.346214148 + 68.0952381 Combine like terms: -114.346214148 + 68.0952381 = -46.250976048 x = -46.250976048 Simplifying x = -46.250976048Solution
The solution to the problem is based on the solutions from the subproblems. x = {182.441452248, -46.250976048}
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