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Simplifying X2 + 700X = 18000 Reorder the terms: 700X + X2 = 18000 Solving 700X + X2 = 18000 Solving for variable 'X'. Reorder the terms: -18000 + 700X + X2 = 18000 + -18000 Combine like terms: 18000 + -18000 = 0 -18000 + 700X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '18000' to each side of the equation. -18000 + 700X + 18000 + X2 = 0 + 18000 Reorder the terms: -18000 + 18000 + 700X + X2 = 0 + 18000 Combine like terms: -18000 + 18000 = 0 0 + 700X + X2 = 0 + 18000 700X + X2 = 0 + 18000 Combine like terms: 0 + 18000 = 18000 700X + X2 = 18000 The X term is 700X. Take half its coefficient (350). Square it (122500) and add it to both sides. Add '122500' to each side of the equation. 700X + 122500 + X2 = 18000 + 122500 Reorder the terms: 122500 + 700X + X2 = 18000 + 122500 Combine like terms: 18000 + 122500 = 140500 122500 + 700X + X2 = 140500 Factor a perfect square on the left side: (X + 350)(X + 350) = 140500 Calculate the square root of the right side: 374.83329628 Break this problem into two subproblems by setting (X + 350) equal to 374.83329628 and -374.83329628.Subproblem 1
X + 350 = 374.83329628 Simplifying X + 350 = 374.83329628 Reorder the terms: 350 + X = 374.83329628 Solving 350 + X = 374.83329628 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-350' to each side of the equation. 350 + -350 + X = 374.83329628 + -350 Combine like terms: 350 + -350 = 0 0 + X = 374.83329628 + -350 X = 374.83329628 + -350 Combine like terms: 374.83329628 + -350 = 24.83329628 X = 24.83329628 Simplifying X = 24.83329628Subproblem 2
X + 350 = -374.83329628 Simplifying X + 350 = -374.83329628 Reorder the terms: 350 + X = -374.83329628 Solving 350 + X = -374.83329628 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-350' to each side of the equation. 350 + -350 + X = -374.83329628 + -350 Combine like terms: 350 + -350 = 0 0 + X = -374.83329628 + -350 X = -374.83329628 + -350 Combine like terms: -374.83329628 + -350 = -724.83329628 X = -724.83329628 Simplifying X = -724.83329628Solution
The solution to the problem is based on the solutions from the subproblems. X = {24.83329628, -724.83329628}
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