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Simplifying a2 + 12a + -21 = 0 Reorder the terms: -21 + 12a + a2 = 0 Solving -21 + 12a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 12a + 21 + a2 = 0 + 21 Reorder the terms: -21 + 21 + 12a + a2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 12a + a2 = 0 + 21 12a + a2 = 0 + 21 Combine like terms: 0 + 21 = 21 12a + a2 = 21 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 = 21 + 36 Reorder the terms: 36 + 12a + a2 = 21 + 36 Combine like terms: 21 + 36 = 57 36 + 12a + a2 = 57 Factor a perfect square on the left side: (a + 6)(a + 6) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (a + 6) equal to 7.549834435 and -7.549834435.Subproblem 1
a + 6 = 7.549834435 Simplifying a + 6 = 7.549834435 Reorder the terms: 6 + a = 7.549834435 Solving 6 + a = 7.549834435 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 = 7.549834435 + -6 Combine like terms: 6 + -6 = 0 0 + a = 7.549834435 + -6 a = 7.549834435 + -6 Combine like terms: 7.549834435 + -6 = 1.549834435 a = 1.549834435 Simplifying a = 1.549834435Subproblem 2
a + 6 = -7.549834435 Simplifying a + 6 = -7.549834435 Reorder the terms: 6 + a = -7.549834435 Solving 6 + a = -7.549834435 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 = -7.549834435 + -6 Combine like terms: 6 + -6 = 0 0 + a = -7.549834435 + -6 a = -7.549834435 + -6 Combine like terms: -7.549834435 + -6 = -13.549834435 a = -13.549834435 Simplifying a = -13.549834435Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.549834435, -13.549834435}
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