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Simplifying a2 + -6a = 13 Reorder the terms: -6a + a2 = 13 Solving -6a + a2 = 13 Solving for variable 'a'. Reorder the terms: -13 + -6a + a2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -6a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -6a + 13 + a2 = 0 + 13 Reorder the terms: -13 + 13 + -6a + a2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -6a + a2 = 0 + 13 -6a + a2 = 0 + 13 Combine like terms: 0 + 13 = 13 -6a + a2 = 13 The a term is -6a. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6a + 9 + a2 = 13 + 9 Reorder the terms: 9 + -6a + a2 = 13 + 9 Combine like terms: 13 + 9 = 22 9 + -6a + a2 = 22 Factor a perfect square on the left side: (a + -3)(a + -3) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (a + -3) equal to 4.69041576 and -4.69041576.Subproblem 1
a + -3 = 4.69041576 Simplifying a + -3 = 4.69041576 Reorder the terms: -3 + a = 4.69041576 Solving -3 + a = 4.69041576 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 4.69041576 + 3 Combine like terms: -3 + 3 = 0 0 + a = 4.69041576 + 3 a = 4.69041576 + 3 Combine like terms: 4.69041576 + 3 = 7.69041576 a = 7.69041576 Simplifying a = 7.69041576Subproblem 2
a + -3 = -4.69041576 Simplifying a + -3 = -4.69041576 Reorder the terms: -3 + a = -4.69041576 Solving -3 + a = -4.69041576 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -4.69041576 + 3 Combine like terms: -3 + 3 = 0 0 + a = -4.69041576 + 3 a = -4.69041576 + 3 Combine like terms: -4.69041576 + 3 = -1.69041576 a = -1.69041576 Simplifying a = -1.69041576Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.69041576, -1.69041576}
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