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Simplifying 2 + -2X2 + -6X = 0 Reorder the terms: 2 + -6X + -2X2 = 0 Solving 2 + -6X + -2X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -3X + -1X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -3X + -1X2)' equal to zero and attempt to solve: Simplifying 1 + -3X + -1X2 = 0 Solving 1 + -3X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + 3X + X2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 3X + 1 + X2 = 0 + 1 Reorder the terms: -1 + 1 + 3X + X2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3X + X2 = 0 + 1 3X + X2 = 0 + 1 Combine like terms: 0 + 1 = 1 3X + X2 = 1 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 = 1 + 2.25 Reorder the terms: 2.25 + 3X + X2 = 1 + 2.25 Combine like terms: 1 + 2.25 = 3.25 2.25 + 3X + X2 = 3.25 Factor a perfect square on the left side: (X + 1.5)(X + 1.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (X + 1.5) equal to 1.802775638 and -1.802775638.Subproblem 1
X + 1.5 = 1.802775638 Simplifying X + 1.5 = 1.802775638 Reorder the terms: 1.5 + X = 1.802775638 Solving 1.5 + X = 1.802775638 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 = 1.802775638 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = 1.802775638 + -1.5 X = 1.802775638 + -1.5 Combine like terms: 1.802775638 + -1.5 = 0.302775638 X = 0.302775638 Simplifying X = 0.302775638Subproblem 2
X + 1.5 = -1.802775638 Simplifying X + 1.5 = -1.802775638 Reorder the terms: 1.5 + X = -1.802775638 Solving 1.5 + X = -1.802775638 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 = -1.802775638 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = -1.802775638 + -1.5 X = -1.802775638 + -1.5 Combine like terms: -1.802775638 + -1.5 = -3.302775638 X = -3.302775638 Simplifying X = -3.302775638Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.302775638, -3.302775638}Solution
X = {0.302775638, -3.302775638}
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