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Simplifying 8460 = x2 + -25x + 50 Reorder the terms: 8460 = 50 + -25x + x2 Solving 8460 = 50 + -25x + x2 Solving for variable 'x'. Combine like terms: 8460 + -50 = 8410 8410 + 25x + -1x2 = 50 + -25x + x2 + -50 + 25x + -1x2 Reorder the terms: 8410 + 25x + -1x2 = 50 + -50 + -25x + 25x + x2 + -1x2 Combine like terms: 50 + -50 = 0 8410 + 25x + -1x2 = 0 + -25x + 25x + x2 + -1x2 8410 + 25x + -1x2 = -25x + 25x + x2 + -1x2 Combine like terms: -25x + 25x = 0 8410 + 25x + -1x2 = 0 + x2 + -1x2 8410 + 25x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 8410 + 25x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8410 + -25x + x2 = 0 Move the constant term to the right: Add '8410' to each side of the equation. -8410 + -25x + 8410 + x2 = 0 + 8410 Reorder the terms: -8410 + 8410 + -25x + x2 = 0 + 8410 Combine like terms: -8410 + 8410 = 0 0 + -25x + x2 = 0 + 8410 -25x + x2 = 0 + 8410 Combine like terms: 0 + 8410 = 8410 -25x + x2 = 8410 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = 8410 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 8410 + 156.25 Combine like terms: 8410 + 156.25 = 8566.25 156.25 + -25x + x2 = 8566.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 8566.25 Calculate the square root of the right side: 92.55403827 Break this problem into two subproblems by setting (x + -12.5) equal to 92.55403827 and -92.55403827.Subproblem 1
x + -12.5 = 92.55403827 Simplifying x + -12.5 = 92.55403827 Reorder the terms: -12.5 + x = 92.55403827 Solving -12.5 + x = 92.55403827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 92.55403827 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 92.55403827 + 12.5 x = 92.55403827 + 12.5 Combine like terms: 92.55403827 + 12.5 = 105.05403827 x = 105.05403827 Simplifying x = 105.05403827Subproblem 2
x + -12.5 = -92.55403827 Simplifying x + -12.5 = -92.55403827 Reorder the terms: -12.5 + x = -92.55403827 Solving -12.5 + x = -92.55403827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -92.55403827 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -92.55403827 + 12.5 x = -92.55403827 + 12.5 Combine like terms: -92.55403827 + 12.5 = -80.05403827 x = -80.05403827 Simplifying x = -80.05403827Solution
The solution to the problem is based on the solutions from the subproblems. x = {105.05403827, -80.05403827}
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