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Simplifying 848x + -1x2 = 169.575 Solving 848x + -1x2 = 169.575 Solving for variable 'x'. Reorder the terms: -169.575 + 848x + -1x2 = 169.575 + -169.575 Combine like terms: 169.575 + -169.575 = 0.000 -169.575 + 848x + -1x2 = 0.000 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 169.575 + -848x + x2 = 0.000 Move the constant term to the right: Add '-169.575' to each side of the equation. 169.575 + -848x + -169.575 + x2 = 0.000 + -169.575 Reorder the terms: 169.575 + -169.575 + -848x + x2 = 0.000 + -169.575 Combine like terms: 169.575 + -169.575 = 0.000 0.000 + -848x + x2 = 0.000 + -169.575 -848x + x2 = 0.000 + -169.575 Combine like terms: 0.000 + -169.575 = -169.575 -848x + x2 = -169.575 The x term is -848x. Take half its coefficient (-424). Square it (179776) and add it to both sides. Add '179776' to each side of the equation. -848x + 179776 + x2 = -169.575 + 179776 Reorder the terms: 179776 + -848x + x2 = -169.575 + 179776 Combine like terms: -169.575 + 179776 = 179606.425 179776 + -848x + x2 = 179606.425 Factor a perfect square on the left side: (x + -424)(x + -424) = 179606.425 Calculate the square root of the right side: 423.799982303 Break this problem into two subproblems by setting (x + -424) equal to 423.799982303 and -423.799982303.Subproblem 1
x + -424 = 423.799982303 Simplifying x + -424 = 423.799982303 Reorder the terms: -424 + x = 423.799982303 Solving -424 + x = 423.799982303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '424' to each side of the equation. -424 + 424 + x = 423.799982303 + 424 Combine like terms: -424 + 424 = 0 0 + x = 423.799982303 + 424 x = 423.799982303 + 424 Combine like terms: 423.799982303 + 424 = 847.799982303 x = 847.799982303 Simplifying x = 847.799982303Subproblem 2
x + -424 = -423.799982303 Simplifying x + -424 = -423.799982303 Reorder the terms: -424 + x = -423.799982303 Solving -424 + x = -423.799982303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '424' to each side of the equation. -424 + 424 + x = -423.799982303 + 424 Combine like terms: -424 + 424 = 0 0 + x = -423.799982303 + 424 x = -423.799982303 + 424 Combine like terms: -423.799982303 + 424 = 0.200017697 x = 0.200017697 Simplifying x = 0.200017697Solution
The solution to the problem is based on the solutions from the subproblems. x = {847.799982303, 0.200017697}
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