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Simplifying a2 + -12a + 5 = 0 Reorder the terms: 5 + -12a + a2 = 0 Solving 5 + -12a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -12a + -5 + a2 = 0 + -5 Reorder the terms: 5 + -5 + -12a + a2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -12a + a2 = 0 + -5 -12a + a2 = 0 + -5 Combine like terms: 0 + -5 = -5 -12a + a2 = -5 The a term is -12a. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12a + 36 + a2 = -5 + 36 Reorder the terms: 36 + -12a + a2 = -5 + 36 Combine like terms: -5 + 36 = 31 36 + -12a + a2 = 31 Factor a perfect square on the left side: (a + -6)(a + -6) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (a + -6) equal to 5.567764363 and -5.567764363.Subproblem 1
a + -6 = 5.567764363 Simplifying a + -6 = 5.567764363 Reorder the terms: -6 + a = 5.567764363 Solving -6 + a = 5.567764363 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = 5.567764363 + 6 Combine like terms: -6 + 6 = 0 0 + a = 5.567764363 + 6 a = 5.567764363 + 6 Combine like terms: 5.567764363 + 6 = 11.567764363 a = 11.567764363 Simplifying a = 11.567764363Subproblem 2
a + -6 = -5.567764363 Simplifying a + -6 = -5.567764363 Reorder the terms: -6 + a = -5.567764363 Solving -6 + a = -5.567764363 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = -5.567764363 + 6 Combine like terms: -6 + 6 = 0 0 + a = -5.567764363 + 6 a = -5.567764363 + 6 Combine like terms: -5.567764363 + 6 = 0.432235637 a = 0.432235637 Simplifying a = 0.432235637Solution
The solution to the problem is based on the solutions from the subproblems. a = {11.567764363, 0.432235637}
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