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Simplifying a2 + -8a + 3 = 0 Reorder the terms: 3 + -8a + a2 = 0 Solving 3 + -8a + a2 = 0 Solving for variable 'a'. 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 = 13 16 + -8a + a2 = 13 Factor a perfect square on the left side: (a + -4)(a + -4) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (a + -4) equal to 3.605551275 and -3.605551275.Subproblem 1
a + -4 = 3.605551275 Simplifying a + -4 = 3.605551275 Reorder the terms: -4 + a = 3.605551275 Solving -4 + a = 3.605551275 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 = 3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + a = 3.605551275 + 4 a = 3.605551275 + 4 Combine like terms: 3.605551275 + 4 = 7.605551275 a = 7.605551275 Simplifying a = 7.605551275Subproblem 2
a + -4 = -3.605551275 Simplifying a + -4 = -3.605551275 Reorder the terms: -4 + a = -3.605551275 Solving -4 + a = -3.605551275 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 = -3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + a = -3.605551275 + 4 a = -3.605551275 + 4 Combine like terms: -3.605551275 + 4 = 0.394448725 a = 0.394448725 Simplifying a = 0.394448725Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.605551275, 0.394448725}
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