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Simplifying x2 + 27x = 400 Reorder the terms: 27x + x2 = 400 Solving 27x + x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 27x + x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 27x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 27x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 27x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 27x + x2 = 0 + 400 27x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 27x + x2 = 400 The x term is 27x. Take half its coefficient (13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. 27x + 182.25 + x2 = 400 + 182.25 Reorder the terms: 182.25 + 27x + x2 = 400 + 182.25 Combine like terms: 400 + 182.25 = 582.25 182.25 + 27x + x2 = 582.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 582.25 Calculate the square root of the right side: 24.129857024 Break this problem into two subproblems by setting (x + 13.5) equal to 24.129857024 and -24.129857024.Subproblem 1
x + 13.5 = 24.129857024 Simplifying x + 13.5 = 24.129857024 Reorder the terms: 13.5 + x = 24.129857024 Solving 13.5 + x = 24.129857024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = 24.129857024 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 24.129857024 + -13.5 x = 24.129857024 + -13.5 Combine like terms: 24.129857024 + -13.5 = 10.629857024 x = 10.629857024 Simplifying x = 10.629857024Subproblem 2
x + 13.5 = -24.129857024 Simplifying x + 13.5 = -24.129857024 Reorder the terms: 13.5 + x = -24.129857024 Solving 13.5 + x = -24.129857024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = -24.129857024 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -24.129857024 + -13.5 x = -24.129857024 + -13.5 Combine like terms: -24.129857024 + -13.5 = -37.629857024 x = -37.629857024 Simplifying x = -37.629857024Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.629857024, -37.629857024}
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