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Simplifying 0 = x2 + 25x + -322 Reorder the terms: 0 = -322 + 25x + x2 Solving 0 = -322 + 25x + x2 Solving for variable 'x'. Combine like terms: 0 + 322 = 322 322 + -25x + -1x2 = -322 + 25x + x2 + 322 + -25x + -1x2 Reorder the terms: 322 + -25x + -1x2 = -322 + 322 + 25x + -25x + x2 + -1x2 Combine like terms: -322 + 322 = 0 322 + -25x + -1x2 = 0 + 25x + -25x + x2 + -1x2 322 + -25x + -1x2 = 25x + -25x + x2 + -1x2 Combine like terms: 25x + -25x = 0 322 + -25x + -1x2 = 0 + x2 + -1x2 322 + -25x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 322 + -25x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -322 + 25x + x2 = 0 Move the constant term to the right: Add '322' to each side of the equation. -322 + 25x + 322 + x2 = 0 + 322 Reorder the terms: -322 + 322 + 25x + x2 = 0 + 322 Combine like terms: -322 + 322 = 0 0 + 25x + x2 = 0 + 322 25x + x2 = 0 + 322 Combine like terms: 0 + 322 = 322 25x + x2 = 322 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 = 322 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 322 + 156.25 Combine like terms: 322 + 156.25 = 478.25 156.25 + 25x + x2 = 478.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 478.25 Calculate the square root of the right side: 21.868927729 Break this problem into two subproblems by setting (x + 12.5) equal to 21.868927729 and -21.868927729.Subproblem 1
x + 12.5 = 21.868927729 Simplifying x + 12.5 = 21.868927729 Reorder the terms: 12.5 + x = 21.868927729 Solving 12.5 + x = 21.868927729 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 = 21.868927729 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 21.868927729 + -12.5 x = 21.868927729 + -12.5 Combine like terms: 21.868927729 + -12.5 = 9.368927729 x = 9.368927729 Simplifying x = 9.368927729Subproblem 2
x + 12.5 = -21.868927729 Simplifying x + 12.5 = -21.868927729 Reorder the terms: 12.5 + x = -21.868927729 Solving 12.5 + x = -21.868927729 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 = -21.868927729 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -21.868927729 + -12.5 x = -21.868927729 + -12.5 Combine like terms: -21.868927729 + -12.5 = -34.368927729 x = -34.368927729 Simplifying x = -34.368927729Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.368927729, -34.368927729}
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