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Simplifying x = 108.8 + -27.2x + x2 Solving x = 108.8 + -27.2x + x2 Solving for variable 'x'. Reorder the terms: -108.8 + x + 27.2x + -1x2 = 108.8 + -27.2x + x2 + -108.8 + 27.2x + -1x2 Combine like terms: x + 27.2x = 28.2x -108.8 + 28.2x + -1x2 = 108.8 + -27.2x + x2 + -108.8 + 27.2x + -1x2 Reorder the terms: -108.8 + 28.2x + -1x2 = 108.8 + -108.8 + -27.2x + 27.2x + x2 + -1x2 Combine like terms: 108.8 + -108.8 = 0.0 -108.8 + 28.2x + -1x2 = 0.0 + -27.2x + 27.2x + x2 + -1x2 -108.8 + 28.2x + -1x2 = -27.2x + 27.2x + x2 + -1x2 Combine like terms: -27.2x + 27.2x = 0.0 -108.8 + 28.2x + -1x2 = 0.0 + x2 + -1x2 -108.8 + 28.2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -108.8 + 28.2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 108.8 + -28.2x + x2 = 0 Move the constant term to the right: Add '-108.8' to each side of the equation. 108.8 + -28.2x + -108.8 + x2 = 0 + -108.8 Reorder the terms: 108.8 + -108.8 + -28.2x + x2 = 0 + -108.8 Combine like terms: 108.8 + -108.8 = 0.0 0.0 + -28.2x + x2 = 0 + -108.8 -28.2x + x2 = 0 + -108.8 Combine like terms: 0 + -108.8 = -108.8 -28.2x + x2 = -108.8 The x term is -28.2x. Take half its coefficient (-14.1). Square it (198.81) and add it to both sides. Add '198.81' to each side of the equation. -28.2x + 198.81 + x2 = -108.8 + 198.81 Reorder the terms: 198.81 + -28.2x + x2 = -108.8 + 198.81 Combine like terms: -108.8 + 198.81 = 90.01 198.81 + -28.2x + x2 = 90.01 Factor a perfect square on the left side: (x + -14.1)(x + -14.1) = 90.01 Calculate the square root of the right side: 9.487360012 Break this problem into two subproblems by setting (x + -14.1) equal to 9.487360012 and -9.487360012.Subproblem 1
x + -14.1 = 9.487360012 Simplifying x + -14.1 = 9.487360012 Reorder the terms: -14.1 + x = 9.487360012 Solving -14.1 + x = 9.487360012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.1' to each side of the equation. -14.1 + 14.1 + x = 9.487360012 + 14.1 Combine like terms: -14.1 + 14.1 = 0.0 0.0 + x = 9.487360012 + 14.1 x = 9.487360012 + 14.1 Combine like terms: 9.487360012 + 14.1 = 23.587360012 x = 23.587360012 Simplifying x = 23.587360012Subproblem 2
x + -14.1 = -9.487360012 Simplifying x + -14.1 = -9.487360012 Reorder the terms: -14.1 + x = -9.487360012 Solving -14.1 + x = -9.487360012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.1' to each side of the equation. -14.1 + 14.1 + x = -9.487360012 + 14.1 Combine like terms: -14.1 + 14.1 = 0.0 0.0 + x = -9.487360012 + 14.1 x = -9.487360012 + 14.1 Combine like terms: -9.487360012 + 14.1 = 4.612639988 x = 4.612639988 Simplifying x = 4.612639988Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.587360012, 4.612639988}
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