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Simplifying 6a + -2a2 + 2 = 0 Reorder the terms: 2 + 6a + -2a2 = 0 Solving 2 + 6a + -2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 3a + -1a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 3a + -1a2)' equal to zero and attempt to solve: Simplifying 1 + 3a + -1a2 = 0 Solving 1 + 3a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -3a + a2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -3a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + -3a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3a + a2 = 0 + 1 -3a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3a + a2 = 1 The a term is -3a. 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. -3a + 2.25 + a2 = 1 + 2.25 Reorder the terms: 2.25 + -3a + a2 = 1 + 2.25 Combine like terms: 1 + 2.25 = 3.25 2.25 + -3a + a2 = 3.25 Factor a perfect square on the left side: (a + -1.5)(a + -1.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (a + -1.5) equal to 1.802775638 and -1.802775638.Subproblem 1
a + -1.5 = 1.802775638 Simplifying a + -1.5 = 1.802775638 Reorder the terms: -1.5 + a = 1.802775638 Solving -1.5 + a = 1.802775638 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = 1.802775638 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 1.802775638 + 1.5 a = 1.802775638 + 1.5 Combine like terms: 1.802775638 + 1.5 = 3.302775638 a = 3.302775638 Simplifying a = 3.302775638Subproblem 2
a + -1.5 = -1.802775638 Simplifying a + -1.5 = -1.802775638 Reorder the terms: -1.5 + a = -1.802775638 Solving -1.5 + a = -1.802775638 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = -1.802775638 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -1.802775638 + 1.5 a = -1.802775638 + 1.5 Combine like terms: -1.802775638 + 1.5 = -0.302775638 a = -0.302775638 Simplifying a = -0.302775638Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.302775638, -0.302775638}Solution
a = {3.302775638, -0.302775638}
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