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Simplifying 4X + X2 = 25 Solving 4X + X2 = 25 Solving for variable 'X'. Reorder the terms: -25 + 4X + X2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 4X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 4X + 25 + X2 = 0 + 25 Reorder the terms: -25 + 25 + 4X + X2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 4X + X2 = 0 + 25 4X + X2 = 0 + 25 Combine like terms: 0 + 25 = 25 4X + X2 = 25 The X term is 4X. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4X + 4 + X2 = 25 + 4 Reorder the terms: 4 + 4X + X2 = 25 + 4 Combine like terms: 25 + 4 = 29 4 + 4X + X2 = 29 Factor a perfect square on the left side: (X + 2)(X + 2) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (X + 2) equal to 5.385164807 and -5.385164807.Subproblem 1
X + 2 = 5.385164807 Simplifying X + 2 = 5.385164807 Reorder the terms: 2 + X = 5.385164807 Solving 2 + X = 5.385164807 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = 5.385164807 + -2 Combine like terms: 2 + -2 = 0 0 + X = 5.385164807 + -2 X = 5.385164807 + -2 Combine like terms: 5.385164807 + -2 = 3.385164807 X = 3.385164807 Simplifying X = 3.385164807Subproblem 2
X + 2 = -5.385164807 Simplifying X + 2 = -5.385164807 Reorder the terms: 2 + X = -5.385164807 Solving 2 + X = -5.385164807 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = -5.385164807 + -2 Combine like terms: 2 + -2 = 0 0 + X = -5.385164807 + -2 X = -5.385164807 + -2 Combine like terms: -5.385164807 + -2 = -7.385164807 X = -7.385164807 Simplifying X = -7.385164807Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.385164807, -7.385164807}
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