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Simplifying (x + -3)(x + -2) = 14 Reorder the terms: (-3 + x)(x + -2) = 14 Reorder the terms: (-3 + x)(-2 + x) = 14 Multiply (-3 + x) * (-2 + x) (-3(-2 + x) + x(-2 + x)) = 14 ((-2 * -3 + x * -3) + x(-2 + x)) = 14 ((6 + -3x) + x(-2 + x)) = 14 (6 + -3x + (-2 * x + x * x)) = 14 (6 + -3x + (-2x + x2)) = 14 Combine like terms: -3x + -2x = -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 = 6.274917218 x = 6.274917218 Simplifying x = 6.274917218Subproblem 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 = -1.274917218 x = -1.274917218 Simplifying x = -1.274917218Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.274917218, -1.274917218}
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