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Simplifying a2 + -12a + 30 = 0 Reorder the terms: 30 + -12a + a2 = 0 Solving 30 + -12a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -12a + -30 + a2 = 0 + -30 Reorder the terms: 30 + -30 + -12a + a2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -12a + a2 = 0 + -30 -12a + a2 = 0 + -30 Combine like terms: 0 + -30 = -30 -12a + a2 = -30 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 = -30 + 36 Reorder the terms: 36 + -12a + a2 = -30 + 36 Combine like terms: -30 + 36 = 6 36 + -12a + a2 = 6 Factor a perfect square on the left side: (a + -6)(a + -6) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (a + -6) equal to 2.449489743 and -2.449489743.Subproblem 1
a + -6 = 2.449489743 Simplifying a + -6 = 2.449489743 Reorder the terms: -6 + a = 2.449489743 Solving -6 + a = 2.449489743 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 = 2.449489743 + 6 Combine like terms: -6 + 6 = 0 0 + a = 2.449489743 + 6 a = 2.449489743 + 6 Combine like terms: 2.449489743 + 6 = 8.449489743 a = 8.449489743 Simplifying a = 8.449489743Subproblem 2
a + -6 = -2.449489743 Simplifying a + -6 = -2.449489743 Reorder the terms: -6 + a = -2.449489743 Solving -6 + a = -2.449489743 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 = -2.449489743 + 6 Combine like terms: -6 + 6 = 0 0 + a = -2.449489743 + 6 a = -2.449489743 + 6 Combine like terms: -2.449489743 + 6 = 3.550510257 a = 3.550510257 Simplifying a = 3.550510257Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.449489743, 3.550510257}
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