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Simplifying x2 + -161.63x + 5857.61 = 0 Reorder the terms: 5857.61 + -161.63x + x2 = 0 Solving 5857.61 + -161.63x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5857.61' to each side of the equation. 5857.61 + -161.63x + -5857.61 + x2 = 0 + -5857.61 Reorder the terms: 5857.61 + -5857.61 + -161.63x + x2 = 0 + -5857.61 Combine like terms: 5857.61 + -5857.61 = 0.00 0.00 + -161.63x + x2 = 0 + -5857.61 -161.63x + x2 = 0 + -5857.61 Combine like terms: 0 + -5857.61 = -5857.61 -161.63x + x2 = -5857.61 The x term is -161.63x. Take half its coefficient (-80.815). Square it (6531.064225) and add it to both sides. Add '6531.064225' to each side of the equation. -161.63x + 6531.064225 + x2 = -5857.61 + 6531.064225 Reorder the terms: 6531.064225 + -161.63x + x2 = -5857.61 + 6531.064225 Combine like terms: -5857.61 + 6531.064225 = 673.454225 6531.064225 + -161.63x + x2 = 673.454225 Factor a perfect square on the left side: (x + -80.815)(x + -80.815) = 673.454225 Calculate the square root of the right side: 25.950996609 Break this problem into two subproblems by setting (x + -80.815) equal to 25.950996609 and -25.950996609.Subproblem 1
x + -80.815 = 25.950996609 Simplifying x + -80.815 = 25.950996609 Reorder the terms: -80.815 + x = 25.950996609 Solving -80.815 + x = 25.950996609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80.815' to each side of the equation. -80.815 + 80.815 + x = 25.950996609 + 80.815 Combine like terms: -80.815 + 80.815 = 0.000 0.000 + x = 25.950996609 + 80.815 x = 25.950996609 + 80.815 Combine like terms: 25.950996609 + 80.815 = 106.765996609 x = 106.765996609 Simplifying x = 106.765996609Subproblem 2
x + -80.815 = -25.950996609 Simplifying x + -80.815 = -25.950996609 Reorder the terms: -80.815 + x = -25.950996609 Solving -80.815 + x = -25.950996609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80.815' to each side of the equation. -80.815 + 80.815 + x = -25.950996609 + 80.815 Combine like terms: -80.815 + 80.815 = 0.000 0.000 + x = -25.950996609 + 80.815 x = -25.950996609 + 80.815 Combine like terms: -25.950996609 + 80.815 = 54.864003391 x = 54.864003391 Simplifying x = 54.864003391Solution
The solution to the problem is based on the solutions from the subproblems. x = {106.765996609, 54.864003391}
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