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Simplifying 3X2 + 12X + -33 = 0 Reorder the terms: -33 + 12X + 3X2 = 0 Solving -33 + 12X + 3X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '3'. 3(-11 + 4X + X2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-11 + 4X + X2)' equal to zero and attempt to solve: Simplifying -11 + 4X + X2 = 0 Solving -11 + 4X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 4X + 11 + X2 = 0 + 11 Reorder the terms: -11 + 11 + 4X + X2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 4X + X2 = 0 + 11 4X + X2 = 0 + 11 Combine like terms: 0 + 11 = 11 4X + X2 = 11 The X term is 4X. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4X + 4 + X2 = 11 + 4 Reorder the terms: 4 + 4X + X2 = 11 + 4 Combine like terms: 11 + 4 = 15 4 + 4X + X2 = 15 Factor a perfect square on the left side: (X + 2)(X + 2) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (X + 2) equal to 3.872983346 and -3.872983346.Subproblem 1
X + 2 = 3.872983346 Simplifying X + 2 = 3.872983346 Reorder the terms: 2 + X = 3.872983346 Solving 2 + X = 3.872983346 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = 3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + X = 3.872983346 + -2 X = 3.872983346 + -2 Combine like terms: 3.872983346 + -2 = 1.872983346 X = 1.872983346 Simplifying X = 1.872983346Subproblem 2
X + 2 = -3.872983346 Simplifying X + 2 = -3.872983346 Reorder the terms: 2 + X = -3.872983346 Solving 2 + X = -3.872983346 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = -3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + X = -3.872983346 + -2 X = -3.872983346 + -2 Combine like terms: -3.872983346 + -2 = -5.872983346 X = -5.872983346 Simplifying X = -5.872983346Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.872983346, -5.872983346}Solution
X = {1.872983346, -5.872983346}
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