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Simplifying X2 + X = 24 Reorder the terms: X + X2 = 24 Solving X + X2 = 24 Solving for variable 'X'. Reorder the terms: -24 + X + X2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + X + 24 + X2 = 0 + 24 Reorder the terms: -24 + 24 + X + X2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + X + X2 = 0 + 24 X + X2 = 0 + 24 Combine like terms: 0 + 24 = 24 X + X2 = 24 The X term is X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. X + 0.25 + X2 = 24 + 0.25 Reorder the terms: 0.25 + X + X2 = 24 + 0.25 Combine like terms: 24 + 0.25 = 24.25 0.25 + X + X2 = 24.25 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (X + 0.5) equal to 4.924428901 and -4.924428901.Subproblem 1
X + 0.5 = 4.924428901 Simplifying X + 0.5 = 4.924428901 Reorder the terms: 0.5 + X = 4.924428901 Solving 0.5 + X = 4.924428901 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 4.924428901 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 4.924428901 + -0.5 X = 4.924428901 + -0.5 Combine like terms: 4.924428901 + -0.5 = 4.424428901 X = 4.424428901 Simplifying X = 4.424428901Subproblem 2
X + 0.5 = -4.924428901 Simplifying X + 0.5 = -4.924428901 Reorder the terms: 0.5 + X = -4.924428901 Solving 0.5 + X = -4.924428901 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -4.924428901 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -4.924428901 + -0.5 X = -4.924428901 + -0.5 Combine like terms: -4.924428901 + -0.5 = -5.424428901 X = -5.424428901 Simplifying X = -5.424428901Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.424428901, -5.424428901}
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