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Simplifying 8000 = x2 + -18x + 56 Reorder the terms: 8000 = 56 + -18x + x2 Solving 8000 = 56 + -18x + x2 Solving for variable 'x'. Combine like terms: 8000 + -56 = 7944 7944 + 18x + -1x2 = 56 + -18x + x2 + -56 + 18x + -1x2 Reorder the terms: 7944 + 18x + -1x2 = 56 + -56 + -18x + 18x + x2 + -1x2 Combine like terms: 56 + -56 = 0 7944 + 18x + -1x2 = 0 + -18x + 18x + x2 + -1x2 7944 + 18x + -1x2 = -18x + 18x + x2 + -1x2 Combine like terms: -18x + 18x = 0 7944 + 18x + -1x2 = 0 + x2 + -1x2 7944 + 18x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7944 + 18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7944 + -18x + x2 = 0 Move the constant term to the right: Add '7944' to each side of the equation. -7944 + -18x + 7944 + x2 = 0 + 7944 Reorder the terms: -7944 + 7944 + -18x + x2 = 0 + 7944 Combine like terms: -7944 + 7944 = 0 0 + -18x + x2 = 0 + 7944 -18x + x2 = 0 + 7944 Combine like terms: 0 + 7944 = 7944 -18x + x2 = 7944 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 7944 + 81 Reorder the terms: 81 + -18x + x2 = 7944 + 81 Combine like terms: 7944 + 81 = 8025 81 + -18x + x2 = 8025 Factor a perfect square on the left side: (x + -9)(x + -9) = 8025 Calculate the square root of the right side: 89.582364336 Break this problem into two subproblems by setting (x + -9) equal to 89.582364336 and -89.582364336.Subproblem 1
x + -9 = 89.582364336 Simplifying x + -9 = 89.582364336 Reorder the terms: -9 + x = 89.582364336 Solving -9 + x = 89.582364336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 89.582364336 + 9 Combine like terms: -9 + 9 = 0 0 + x = 89.582364336 + 9 x = 89.582364336 + 9 Combine like terms: 89.582364336 + 9 = 98.582364336 x = 98.582364336 Simplifying x = 98.582364336Subproblem 2
x + -9 = -89.582364336 Simplifying x + -9 = -89.582364336 Reorder the terms: -9 + x = -89.582364336 Solving -9 + x = -89.582364336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -89.582364336 + 9 Combine like terms: -9 + 9 = 0 0 + x = -89.582364336 + 9 x = -89.582364336 + 9 Combine like terms: -89.582364336 + 9 = -80.582364336 x = -80.582364336 Simplifying x = -80.582364336Solution
The solution to the problem is based on the solutions from the subproblems. x = {98.582364336, -80.582364336}
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