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Simplifying 0.0021(x2) + -0.3592(x) + -14.663 = 0 Reorder the terms: -14.663 + -0.3592x + 0.0021x2 = 0 Solving -14.663 + -0.3592x + 0.0021x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0021 the coefficient of the squared term: Divide each side by '0.0021'. -6982.380952 + -171.047619x + x2 = 0 Move the constant term to the right: Add '6982.380952' to each side of the equation. -6982.380952 + -171.047619x + 6982.380952 + x2 = 0 + 6982.380952 Reorder the terms: -6982.380952 + 6982.380952 + -171.047619x + x2 = 0 + 6982.380952 Combine like terms: -6982.380952 + 6982.380952 = 0.000000 0.000000 + -171.047619x + x2 = 0 + 6982.380952 -171.047619x + x2 = 0 + 6982.380952 Combine like terms: 0 + 6982.380952 = 6982.380952 -171.047619x + x2 = 6982.380952 The x term is -171.047619x. Take half its coefficient (-85.5238095). Square it (7314.321991) and add it to both sides. Add '7314.321991' to each side of the equation. -171.047619x + 7314.321991 + x2 = 6982.380952 + 7314.321991 Reorder the terms: 7314.321991 + -171.047619x + x2 = 6982.380952 + 7314.321991 Combine like terms: 6982.380952 + 7314.321991 = 14296.702943 7314.321991 + -171.047619x + x2 = 14296.702943 Factor a perfect square on the left side: (x + -85.5238095)(x + -85.5238095) = 14296.702943 Calculate the square root of the right side: 119.568820948 Break this problem into two subproblems by setting (x + -85.5238095) equal to 119.568820948 and -119.568820948.Subproblem 1
x + -85.5238095 = 119.568820948 Simplifying x + -85.5238095 = 119.568820948 Reorder the terms: -85.5238095 + x = 119.568820948 Solving -85.5238095 + x = 119.568820948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '85.5238095' to each side of the equation. -85.5238095 + 85.5238095 + x = 119.568820948 + 85.5238095 Combine like terms: -85.5238095 + 85.5238095 = 0.0000000 0.0000000 + x = 119.568820948 + 85.5238095 x = 119.568820948 + 85.5238095 Combine like terms: 119.568820948 + 85.5238095 = 205.092630448 x = 205.092630448 Simplifying x = 205.092630448Subproblem 2
x + -85.5238095 = -119.568820948 Simplifying x + -85.5238095 = -119.568820948 Reorder the terms: -85.5238095 + x = -119.568820948 Solving -85.5238095 + x = -119.568820948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '85.5238095' to each side of the equation. -85.5238095 + 85.5238095 + x = -119.568820948 + 85.5238095 Combine like terms: -85.5238095 + 85.5238095 = 0.0000000 0.0000000 + x = -119.568820948 + 85.5238095 x = -119.568820948 + 85.5238095 Combine like terms: -119.568820948 + 85.5238095 = -34.045011448 x = -34.045011448 Simplifying x = -34.045011448Solution
The solution to the problem is based on the solutions from the subproblems. x = {205.092630448, -34.045011448}
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