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Simplifying 2a2 + -2a + -3 = a2 + 6a Reorder the terms: -3 + -2a + 2a2 = a2 + 6a Reorder the terms: -3 + -2a + 2a2 = 6a + a2 Solving -3 + -2a + 2a2 = 6a + a2 Solving for variable 'a'. Reorder the terms: -3 + -2a + -6a + 2a2 + -1a2 = 6a + a2 + -6a + -1a2 Combine like terms: -2a + -6a = -8a -3 + -8a + 2a2 + -1a2 = 6a + a2 + -6a + -1a2 Combine like terms: 2a2 + -1a2 = 1a2 -3 + -8a + 1a2 = 6a + a2 + -6a + -1a2 Reorder the terms: -3 + -8a + 1a2 = 6a + -6a + a2 + -1a2 Combine like terms: 6a + -6a = 0 -3 + -8a + 1a2 = 0 + a2 + -1a2 -3 + -8a + 1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 -3 + -8a + 1a2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -8a + 3 + a2 = 0 + 3 Reorder the terms: -3 + 3 + -8a + a2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8a + a2 = 0 + 3 -8a + a2 = 0 + 3 Combine like terms: 0 + 3 = 3 -8a + a2 = 3 The a term is -8a. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8a + 16 + a2 = 3 + 16 Reorder the terms: 16 + -8a + a2 = 3 + 16 Combine like terms: 3 + 16 = 19 16 + -8a + a2 = 19 Factor a perfect square on the left side: (a + -4)(a + -4) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (a + -4) equal to 4.358898944 and -4.358898944.Subproblem 1
a + -4 = 4.358898944 Simplifying a + -4 = 4.358898944 Reorder the terms: -4 + a = 4.358898944 Solving -4 + a = 4.358898944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = 4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + a = 4.358898944 + 4 a = 4.358898944 + 4 Combine like terms: 4.358898944 + 4 = 8.358898944 a = 8.358898944 Simplifying a = 8.358898944Subproblem 2
a + -4 = -4.358898944 Simplifying a + -4 = -4.358898944 Reorder the terms: -4 + a = -4.358898944 Solving -4 + a = -4.358898944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = -4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + a = -4.358898944 + 4 a = -4.358898944 + 4 Combine like terms: -4.358898944 + 4 = -0.358898944 a = -0.358898944 Simplifying a = -0.358898944Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.358898944, -0.358898944}
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