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Simplifying X2 + -6X = 14 Reorder the terms: -6X + X2 = 14 Solving -6X + X2 = 14 Solving for variable 'X'. Reorder the terms: -14 + -6X + X2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -6X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -6X + 14 + X2 = 0 + 14 Reorder the terms: -14 + 14 + -6X + X2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -6X + X2 = 0 + 14 -6X + X2 = 0 + 14 Combine like terms: 0 + 14 = 14 -6X + X2 = 14 The X term is -6X. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6X + 9 + X2 = 14 + 9 Reorder the terms: 9 + -6X + X2 = 14 + 9 Combine like terms: 14 + 9 = 23 9 + -6X + X2 = 23 Factor a perfect square on the left side: (X + -3)(X + -3) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (X + -3) equal to 4.795831523 and -4.795831523.Subproblem 1
X + -3 = 4.795831523 Simplifying X + -3 = 4.795831523 Reorder the terms: -3 + X = 4.795831523 Solving -3 + X = 4.795831523 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = 4.795831523 + 3 Combine like terms: -3 + 3 = 0 0 + X = 4.795831523 + 3 X = 4.795831523 + 3 Combine like terms: 4.795831523 + 3 = 7.795831523 X = 7.795831523 Simplifying X = 7.795831523Subproblem 2
X + -3 = -4.795831523 Simplifying X + -3 = -4.795831523 Reorder the terms: -3 + X = -4.795831523 Solving -3 + X = -4.795831523 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = -4.795831523 + 3 Combine like terms: -3 + 3 = 0 0 + X = -4.795831523 + 3 X = -4.795831523 + 3 Combine like terms: -4.795831523 + 3 = -1.795831523 X = -1.795831523 Simplifying X = -1.795831523Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.795831523, -1.795831523}
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