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Simplifying 2a2 + 6a + -4 = 0 Reorder the terms: -4 + 6a + 2a2 = 0 Solving -4 + 6a + 2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 3a + a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 3a + a2)' equal to zero and attempt to solve: Simplifying -2 + 3a + a2 = 0 Solving -2 + 3a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 3a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + 3a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3a + a2 = 0 + 2 3a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 3a + a2 = 2 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 = 2 + 2.25 Reorder the terms: 2.25 + 3a + a2 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + 3a + a2 = 4.25 Factor a perfect square on the left side: (a + 1.5)(a + 1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (a + 1.5) equal to 2.061552813 and -2.061552813.Subproblem 1
a + 1.5 = 2.061552813 Simplifying a + 1.5 = 2.061552813 Reorder the terms: 1.5 + a = 2.061552813 Solving 1.5 + a = 2.061552813 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 = 2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 2.061552813 + -1.5 a = 2.061552813 + -1.5 Combine like terms: 2.061552813 + -1.5 = 0.561552813 a = 0.561552813 Simplifying a = 0.561552813Subproblem 2
a + 1.5 = -2.061552813 Simplifying a + 1.5 = -2.061552813 Reorder the terms: 1.5 + a = -2.061552813 Solving 1.5 + a = -2.061552813 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 = -2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -2.061552813 + -1.5 a = -2.061552813 + -1.5 Combine like terms: -2.061552813 + -1.5 = -3.561552813 a = -3.561552813 Simplifying a = -3.561552813Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.561552813, -3.561552813}Solution
a = {0.561552813, -3.561552813}
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