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Simplifying (x + 2)(x + 3) = 14 Reorder the terms: (2 + x)(x + 3) = 14 Reorder the terms: (2 + x)(3 + x) = 14 Multiply (2 + x) * (3 + x) (2(3 + x) + x(3 + x)) = 14 ((3 * 2 + x * 2) + x(3 + x)) = 14 ((6 + 2x) + x(3 + x)) = 14 (6 + 2x + (3 * x + x * x)) = 14 (6 + 2x + (3x + x2)) = 14 Combine like terms: 2x + 3x = 5x (6 + 5x + x2) = 14 Solving 6 + 5x + x2 = 14 Solving for variable 'x'. Reorder the terms: 6 + -14 + 5x + x2 = 14 + -14 Combine like terms: 6 + -14 = -8 -8 + 5x + x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -8 + 5x + x2 = 0 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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