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Simplifying x2 = -24 + 108x Solving x2 = -24 + 108x Solving for variable 'x'. Reorder the terms: 24 + -108x + x2 = -24 + 108x + 24 + -108x Reorder the terms: 24 + -108x + x2 = -24 + 24 + 108x + -108x Combine like terms: -24 + 24 = 0 24 + -108x + x2 = 0 + 108x + -108x 24 + -108x + x2 = 108x + -108x Combine like terms: 108x + -108x = 0 24 + -108x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -108x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + -108x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -108x + x2 = 0 + -24 -108x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 -108x + x2 = -24 The x term is -108x. Take half its coefficient (-54). Square it (2916) and add it to both sides. Add '2916' to each side of the equation. -108x + 2916 + x2 = -24 + 2916 Reorder the terms: 2916 + -108x + x2 = -24 + 2916 Combine like terms: -24 + 2916 = 2892 2916 + -108x + x2 = 2892 Factor a perfect square on the left side: (x + -54)(x + -54) = 2892 Calculate the square root of the right side: 53.777318639 Break this problem into two subproblems by setting (x + -54) equal to 53.777318639 and -53.777318639.Subproblem 1
x + -54 = 53.777318639 Simplifying x + -54 = 53.777318639 Reorder the terms: -54 + x = 53.777318639 Solving -54 + x = 53.777318639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '54' to each side of the equation. -54 + 54 + x = 53.777318639 + 54 Combine like terms: -54 + 54 = 0 0 + x = 53.777318639 + 54 x = 53.777318639 + 54 Combine like terms: 53.777318639 + 54 = 107.777318639 x = 107.777318639 Simplifying x = 107.777318639Subproblem 2
x + -54 = -53.777318639 Simplifying x + -54 = -53.777318639 Reorder the terms: -54 + x = -53.777318639 Solving -54 + x = -53.777318639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '54' to each side of the equation. -54 + 54 + x = -53.777318639 + 54 Combine like terms: -54 + 54 = 0 0 + x = -53.777318639 + 54 x = -53.777318639 + 54 Combine like terms: -53.777318639 + 54 = 0.222681361 x = 0.222681361 Simplifying x = 0.222681361Solution
The solution to the problem is based on the solutions from the subproblems. x = {107.777318639, 0.222681361}
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