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Simplifying (X + 3)(X + 2) + -14 = 0 Reorder the terms: (3 + X)(X + 2) + -14 = 0 Reorder the terms: (3 + X)(2 + X) + -14 = 0 Multiply (3 + X) * (2 + X) (3(2 + X) + X(2 + X)) + -14 = 0 ((2 * 3 + X * 3) + X(2 + X)) + -14 = 0 ((6 + 3X) + X(2 + X)) + -14 = 0 (6 + 3X + (2 * X + X * X)) + -14 = 0 (6 + 3X + (2X + X2)) + -14 = 0 Combine like terms: 3X + 2X = 5X (6 + 5X + X2) + -14 = 0 Reorder the terms: 6 + -14 + 5X + X2 = 0 Combine like terms: 6 + -14 = -8 -8 + 5X + X2 = 0 Solving -8 + 5X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 5X + 8 + X2 = 0 + 8 Reorder the terms: -8 + 8 + 5X + X2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 5X + X2 = 0 + 8 5X + X2 = 0 + 8 Combine like terms: 0 + 8 = 8 5X + X2 = 8 The X term is 5X. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5X + 6.25 + X2 = 8 + 6.25 Reorder the terms: 6.25 + 5X + X2 = 8 + 6.25 Combine like terms: 8 + 6.25 = 14.25 6.25 + 5X + X2 = 14.25 Factor a perfect square on the left side: (X + 2.5)(X + 2.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (X + 2.5) equal to 3.774917218 and -3.774917218.Subproblem 1
X + 2.5 = 3.774917218 Simplifying X + 2.5 = 3.774917218 Reorder the terms: 2.5 + X = 3.774917218 Solving 2.5 + X = 3.774917218 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + X = 3.774917218 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = 3.774917218 + -2.5 X = 3.774917218 + -2.5 Combine like terms: 3.774917218 + -2.5 = 1.274917218 X = 1.274917218 Simplifying X = 1.274917218Subproblem 2
X + 2.5 = -3.774917218 Simplifying X + 2.5 = -3.774917218 Reorder the terms: 2.5 + X = -3.774917218 Solving 2.5 + X = -3.774917218 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + X = -3.774917218 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = -3.774917218 + -2.5 X = -3.774917218 + -2.5 Combine like terms: -3.774917218 + -2.5 = -6.274917218 X = -6.274917218 Simplifying X = -6.274917218Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.274917218, -6.274917218}
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