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Simplifying 6x2 + -19x + -164 = 0 Reorder the terms: -164 + -19x + 6x2 = 0 Solving -164 + -19x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -27.33333333 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '27.33333333' to each side of the equation. -27.33333333 + -3.166666667x + 27.33333333 + x2 = 0 + 27.33333333 Reorder the terms: -27.33333333 + 27.33333333 + -3.166666667x + x2 = 0 + 27.33333333 Combine like terms: -27.33333333 + 27.33333333 = 0.00000000 0.00000000 + -3.166666667x + x2 = 0 + 27.33333333 -3.166666667x + x2 = 0 + 27.33333333 Combine like terms: 0 + 27.33333333 = 27.33333333 -3.166666667x + x2 = 27.33333333 The x term is -3.166666667x. Take half its coefficient (-1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. -3.166666667x + 2.506944447 + x2 = 27.33333333 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = 27.33333333 + 2.506944447 Combine like terms: 27.33333333 + 2.506944447 = 29.840277777 2.506944447 + -3.166666667x + x2 = 29.840277777 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 29.840277777 Calculate the square root of the right side: 5.462625539 Break this problem into two subproblems by setting (x + -1.583333334) equal to 5.462625539 and -5.462625539.Subproblem 1
x + -1.583333334 = 5.462625539 Simplifying x + -1.583333334 = 5.462625539 Reorder the terms: -1.583333334 + x = 5.462625539 Solving -1.583333334 + x = 5.462625539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = 5.462625539 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 5.462625539 + 1.583333334 x = 5.462625539 + 1.583333334 Combine like terms: 5.462625539 + 1.583333334 = 7.045958873 x = 7.045958873 Simplifying x = 7.045958873Subproblem 2
x + -1.583333334 = -5.462625539 Simplifying x + -1.583333334 = -5.462625539 Reorder the terms: -1.583333334 + x = -5.462625539 Solving -1.583333334 + x = -5.462625539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = -5.462625539 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -5.462625539 + 1.583333334 x = -5.462625539 + 1.583333334 Combine like terms: -5.462625539 + 1.583333334 = -3.879292205 x = -3.879292205 Simplifying x = -3.879292205Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.045958873, -3.879292205}
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