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Simplifying 3X2 + 9X = 36 Reorder the terms: 9X + 3X2 = 36 Solving 9X + 3X2 = 36 Solving for variable 'X'. Reorder the terms: -36 + 9X + 3X2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 9X + 3X2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-12 + 3X + X2) = 0 Ignore the factor 3.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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