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Simplifying 5X2 + 10X + X + -2X + X2 + -6 + 3X = 0 Reorder the terms: -6 + 10X + X + -2X + 3X + 5X2 + X2 = 0 Combine like terms: 10X + X = 11X -6 + 11X + -2X + 3X + 5X2 + X2 = 0 Combine like terms: 11X + -2X = 9X -6 + 9X + 3X + 5X2 + X2 = 0 Combine like terms: 9X + 3X = 12X -6 + 12X + 5X2 + X2 = 0 Combine like terms: 5X2 + X2 = 6X2 -6 + 12X + 6X2 = 0 Solving -6 + 12X + 6X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '6'. 6(-1 + 2X + X2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-1 + 2X + X2)' equal to zero and attempt to solve: Simplifying -1 + 2X + X2 = 0 Solving -1 + 2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 2X + 1 + X2 = 0 + 1 Reorder the terms: -1 + 1 + 2X + X2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2X + X2 = 0 + 1 2X + X2 = 0 + 1 Combine like terms: 0 + 1 = 1 2X + X2 = 1 The X term is 2X. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2X + 1 + X2 = 1 + 1 Reorder the terms: 1 + 2X + X2 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + 2X + X2 = 2 Factor a perfect square on the left side: (X + 1)(X + 1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (X + 1) equal to 1.414213562 and -1.414213562.Subproblem 1
X + 1 = 1.414213562 Simplifying X + 1 = 1.414213562 Reorder the terms: 1 + X = 1.414213562 Solving 1 + X = 1.414213562 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = 1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + X = 1.414213562 + -1 X = 1.414213562 + -1 Combine like terms: 1.414213562 + -1 = 0.414213562 X = 0.414213562 Simplifying X = 0.414213562Subproblem 2
X + 1 = -1.414213562 Simplifying X + 1 = -1.414213562 Reorder the terms: 1 + X = -1.414213562 Solving 1 + X = -1.414213562 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + X = -1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + X = -1.414213562 + -1 X = -1.414213562 + -1 Combine like terms: -1.414213562 + -1 = -2.414213562 X = -2.414213562 Simplifying X = -2.414213562Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.414213562, -2.414213562}Solution
X = {0.414213562, -2.414213562}
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