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Simplifying 6 + 2X + X2 = 20 Solving 6 + 2X + X2 = 20 Solving for variable 'X'. Reorder the terms: 6 + -20 + 2X + X2 = 20 + -20 Combine like terms: 6 + -20 = -14 -14 + 2X + X2 = 20 + -20 Combine like terms: 20 + -20 = 0 -14 + 2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 2X + 14 + X2 = 0 + 14 Reorder the terms: -14 + 14 + 2X + X2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 2X + X2 = 0 + 14 2X + X2 = 0 + 14 Combine like terms: 0 + 14 = 14 2X + X2 = 14 The X term is 2X. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2X + 1 + X2 = 14 + 1 Reorder the terms: 1 + 2X + X2 = 14 + 1 Combine like terms: 14 + 1 = 15 1 + 2X + X2 = 15 Factor a perfect square on the left side: (X + 1)(X + 1) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (X + 1) equal to 3.872983346 and -3.872983346.Subproblem 1
X + 1 = 3.872983346 Simplifying X + 1 = 3.872983346 Reorder the terms: 1 + X = 3.872983346 Solving 1 + X = 3.872983346 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = 3.872983346 + -1 Combine like terms: 1 + -1 = 0 0 + X = 3.872983346 + -1 X = 3.872983346 + -1 Combine like terms: 3.872983346 + -1 = 2.872983346 X = 2.872983346 Simplifying X = 2.872983346Subproblem 2
X + 1 = -3.872983346 Simplifying X + 1 = -3.872983346 Reorder the terms: 1 + X = -3.872983346 Solving 1 + X = -3.872983346 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = -3.872983346 + -1 Combine like terms: 1 + -1 = 0 0 + X = -3.872983346 + -1 X = -3.872983346 + -1 Combine like terms: -3.872983346 + -1 = -4.872983346 X = -4.872983346 Simplifying X = -4.872983346Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.872983346, -4.872983346}
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