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Simplifying (X + -3)(X + -4) = 14 Reorder the terms: (-3 + X)(X + -4) = 14 Reorder the terms: (-3 + X)(-4 + X) = 14 Multiply (-3 + X) * (-4 + X) (-3(-4 + X) + X(-4 + X)) = 14 ((-4 * -3 + X * -3) + X(-4 + X)) = 14 ((12 + -3X) + X(-4 + X)) = 14 (12 + -3X + (-4 * X + X * X)) = 14 (12 + -3X + (-4X + X2)) = 14 Combine like terms: -3X + -4X = -7X (12 + -7X + X2) = 14 Solving 12 + -7X + X2 = 14 Solving for variable 'X'. Reorder the terms: 12 + -14 + -7X + X2 = 14 + -14 Combine like terms: 12 + -14 = -2 -2 + -7X + X2 = 14 + -14 Combine like terms: 14 + -14 = 0 -2 + -7X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -7X + 2 + X2 = 0 + 2 Reorder the terms: -2 + 2 + -7X + X2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -7X + X2 = 0 + 2 -7X + X2 = 0 + 2 Combine like terms: 0 + 2 = 2 -7X + X2 = 2 The X term is -7X. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7X + 12.25 + X2 = 2 + 12.25 Reorder the terms: 12.25 + -7X + X2 = 2 + 12.25 Combine like terms: 2 + 12.25 = 14.25 12.25 + -7X + X2 = 14.25 Factor a perfect square on the left side: (X + -3.5)(X + -3.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (X + -3.5) equal to 3.774917218 and -3.774917218.Subproblem 1
X + -3.5 = 3.774917218 Simplifying X + -3.5 = 3.774917218 Reorder the terms: -3.5 + X = 3.774917218 Solving -3.5 + X = 3.774917218 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + X = 3.774917218 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + X = 3.774917218 + 3.5 X = 3.774917218 + 3.5 Combine like terms: 3.774917218 + 3.5 = 7.274917218 X = 7.274917218 Simplifying X = 7.274917218Subproblem 2
X + -3.5 = -3.774917218 Simplifying X + -3.5 = -3.774917218 Reorder the terms: -3.5 + X = -3.774917218 Solving -3.5 + X = -3.774917218 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + X = -3.774917218 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + X = -3.774917218 + 3.5 X = -3.774917218 + 3.5 Combine like terms: -3.774917218 + 3.5 = -0.274917218 X = -0.274917218 Simplifying X = -0.274917218Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.274917218, -0.274917218}
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