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Simplifying 2x(3 + x) = 24 (3 * 2x + x * 2x) = 24 (6x + 2x2) = 24 Solving 6x + 2x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + 6x + 2x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 3x + x2)' equal to zero and attempt to solve: Simplifying -12 + 3x + x2 = 0 Solving -12 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 3x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 3x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 3x + x2 = 0 + 12 3x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 3x + x2 = 12 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 12 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 12 + 2.25 Combine like terms: 12 + 2.25 = 14.25 2.25 + 3x + x2 = 14.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + 1.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + 1.5 = 3.774917218 Simplifying x + 1.5 = 3.774917218 Reorder the terms: 1.5 + x = 3.774917218 Solving 1.5 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 3.774917218 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.774917218 + -1.5 x = 3.774917218 + -1.5 Combine like terms: 3.774917218 + -1.5 = 2.274917218 x = 2.274917218 Simplifying x = 2.274917218Subproblem 2
x + 1.5 = -3.774917218 Simplifying x + 1.5 = -3.774917218 Reorder the terms: 1.5 + x = -3.774917218 Solving 1.5 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -3.774917218 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.774917218 + -1.5 x = -3.774917218 + -1.5 Combine like terms: -3.774917218 + -1.5 = -5.274917218 x = -5.274917218 Simplifying x = -5.274917218Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.274917218, -5.274917218}Solution
x = {2.274917218, -5.274917218}
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