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Simplifying X2 + (7 + -1X) = 25 Remove parenthesis around (7 + -1X) X2 + 7 + -1X = 25 Reorder the terms: 7 + -1X + X2 = 25 Solving 7 + -1X + X2 = 25 Solving for variable 'X'. Reorder the terms: 7 + -25 + -1X + X2 = 25 + -25 Combine like terms: 7 + -25 = -18 -18 + -1X + X2 = 25 + -25 Combine like terms: 25 + -25 = 0 -18 + -1X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -1X + 18 + X2 = 0 + 18 Reorder the terms: -18 + 18 + -1X + X2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1X + X2 = 0 + 18 -1X + X2 = 0 + 18 Combine like terms: 0 + 18 = 18 -1X + X2 = 18 The X term is -1X. 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. -1X + 0.25 + X2 = 18 + 0.25 Reorder the terms: 0.25 + -1X + X2 = 18 + 0.25 Combine like terms: 18 + 0.25 = 18.25 0.25 + -1X + X2 = 18.25 Factor a perfect square on the left side: (X + -0.5)(X + -0.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (X + -0.5) equal to 4.272001873 and -4.272001873.Subproblem 1
X + -0.5 = 4.272001873 Simplifying X + -0.5 = 4.272001873 Reorder the terms: -0.5 + X = 4.272001873 Solving -0.5 + X = 4.272001873 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 = 4.272001873 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = 4.272001873 + 0.5 X = 4.272001873 + 0.5 Combine like terms: 4.272001873 + 0.5 = 4.772001873 X = 4.772001873 Simplifying X = 4.772001873Subproblem 2
X + -0.5 = -4.272001873 Simplifying X + -0.5 = -4.272001873 Reorder the terms: -0.5 + X = -4.272001873 Solving -0.5 + X = -4.272001873 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 = -4.272001873 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = -4.272001873 + 0.5 X = -4.272001873 + 0.5 Combine like terms: -4.272001873 + 0.5 = -3.772001873 X = -3.772001873 Simplifying X = -3.772001873Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.772001873, -3.772001873}
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