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Simplifying 2400 = 105x + -30 + -1x2 Reorder the terms: 2400 = -30 + 105x + -1x2 Solving 2400 = -30 + 105x + -1x2 Solving for variable 'x'. Combine like terms: 2400 + 30 = 2430 2430 + -105x + x2 = -30 + 105x + -1x2 + 30 + -105x + x2 Reorder the terms: 2430 + -105x + x2 = -30 + 30 + 105x + -105x + -1x2 + x2 Combine like terms: -30 + 30 = 0 2430 + -105x + x2 = 0 + 105x + -105x + -1x2 + x2 2430 + -105x + x2 = 105x + -105x + -1x2 + x2 Combine like terms: 105x + -105x = 0 2430 + -105x + x2 = 0 + -1x2 + x2 2430 + -105x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 2430 + -105x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2430' to each side of the equation. 2430 + -105x + -2430 + x2 = 0 + -2430 Reorder the terms: 2430 + -2430 + -105x + x2 = 0 + -2430 Combine like terms: 2430 + -2430 = 0 0 + -105x + x2 = 0 + -2430 -105x + x2 = 0 + -2430 Combine like terms: 0 + -2430 = -2430 -105x + x2 = -2430 The x term is -105x. Take half its coefficient (-52.5). Square it (2756.25) and add it to both sides. Add '2756.25' to each side of the equation. -105x + 2756.25 + x2 = -2430 + 2756.25 Reorder the terms: 2756.25 + -105x + x2 = -2430 + 2756.25 Combine like terms: -2430 + 2756.25 = 326.25 2756.25 + -105x + x2 = 326.25 Factor a perfect square on the left side: (x + -52.5)(x + -52.5) = 326.25 Calculate the square root of the right side: 18.062391868 Break this problem into two subproblems by setting (x + -52.5) equal to 18.062391868 and -18.062391868.Subproblem 1
x + -52.5 = 18.062391868 Simplifying x + -52.5 = 18.062391868 Reorder the terms: -52.5 + x = 18.062391868 Solving -52.5 + x = 18.062391868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52.5' to each side of the equation. -52.5 + 52.5 + x = 18.062391868 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + x = 18.062391868 + 52.5 x = 18.062391868 + 52.5 Combine like terms: 18.062391868 + 52.5 = 70.562391868 x = 70.562391868 Simplifying x = 70.562391868Subproblem 2
x + -52.5 = -18.062391868 Simplifying x + -52.5 = -18.062391868 Reorder the terms: -52.5 + x = -18.062391868 Solving -52.5 + x = -18.062391868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52.5' to each side of the equation. -52.5 + 52.5 + x = -18.062391868 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + x = -18.062391868 + 52.5 x = -18.062391868 + 52.5 Combine like terms: -18.062391868 + 52.5 = 34.437608132 x = 34.437608132 Simplifying x = 34.437608132Solution
The solution to the problem is based on the solutions from the subproblems. x = {70.562391868, 34.437608132}
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