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Simplifying 862x + -1x2 = 171873 Solving 862x + -1x2 = 171873 Solving for variable 'x'. Reorder the terms: -171873 + 862x + -1x2 = 171873 + -171873 Combine like terms: 171873 + -171873 = 0 -171873 + 862x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 171873 + -862x + x2 = 0 Move the constant term to the right: Add '-171873' to each side of the equation. 171873 + -862x + -171873 + x2 = 0 + -171873 Reorder the terms: 171873 + -171873 + -862x + x2 = 0 + -171873 Combine like terms: 171873 + -171873 = 0 0 + -862x + x2 = 0 + -171873 -862x + x2 = 0 + -171873 Combine like terms: 0 + -171873 = -171873 -862x + x2 = -171873 The x term is -862x. Take half its coefficient (-431). Square it (185761) and add it to both sides. Add '185761' to each side of the equation. -862x + 185761 + x2 = -171873 + 185761 Reorder the terms: 185761 + -862x + x2 = -171873 + 185761 Combine like terms: -171873 + 185761 = 13888 185761 + -862x + x2 = 13888 Factor a perfect square on the left side: (x + -431)(x + -431) = 13888 Calculate the square root of the right side: 117.847358901 Break this problem into two subproblems by setting (x + -431) equal to 117.847358901 and -117.847358901.Subproblem 1
x + -431 = 117.847358901 Simplifying x + -431 = 117.847358901 Reorder the terms: -431 + x = 117.847358901 Solving -431 + x = 117.847358901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '431' to each side of the equation. -431 + 431 + x = 117.847358901 + 431 Combine like terms: -431 + 431 = 0 0 + x = 117.847358901 + 431 x = 117.847358901 + 431 Combine like terms: 117.847358901 + 431 = 548.847358901 x = 548.847358901 Simplifying x = 548.847358901Subproblem 2
x + -431 = -117.847358901 Simplifying x + -431 = -117.847358901 Reorder the terms: -431 + x = -117.847358901 Solving -431 + x = -117.847358901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '431' to each side of the equation. -431 + 431 + x = -117.847358901 + 431 Combine like terms: -431 + 431 = 0 0 + x = -117.847358901 + 431 x = -117.847358901 + 431 Combine like terms: -117.847358901 + 431 = 313.152641099 x = 313.152641099 Simplifying x = 313.152641099Solution
The solution to the problem is based on the solutions from the subproblems. x = {548.847358901, 313.152641099}
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