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Simplifying -1a2 + -4a + 9 = 0 Reorder the terms: 9 + -4a + -1a2 = 0 Solving 9 + -4a + -1a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + 4a + a2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 4a + 9 + a2 = 0 + 9 Reorder the terms: -9 + 9 + 4a + a2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4a + a2 = 0 + 9 4a + a2 = 0 + 9 Combine like terms: 0 + 9 = 9 4a + a2 = 9 The a term is 4a. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4a + 4 + a2 = 9 + 4 Reorder the terms: 4 + 4a + a2 = 9 + 4 Combine like terms: 9 + 4 = 13 4 + 4a + a2 = 13 Factor a perfect square on the left side: (a + 2)(a + 2) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (a + 2) equal to 3.605551275 and -3.605551275.Subproblem 1
a + 2 = 3.605551275 Simplifying a + 2 = 3.605551275 Reorder the terms: 2 + a = 3.605551275 Solving 2 + a = 3.605551275 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 3.605551275 + -2 Combine like terms: 2 + -2 = 0 0 + a = 3.605551275 + -2 a = 3.605551275 + -2 Combine like terms: 3.605551275 + -2 = 1.605551275 a = 1.605551275 Simplifying a = 1.605551275Subproblem 2
a + 2 = -3.605551275 Simplifying a + 2 = -3.605551275 Reorder the terms: 2 + a = -3.605551275 Solving 2 + a = -3.605551275 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = -3.605551275 + -2 Combine like terms: 2 + -2 = 0 0 + a = -3.605551275 + -2 a = -3.605551275 + -2 Combine like terms: -3.605551275 + -2 = -5.605551275 a = -5.605551275 Simplifying a = -5.605551275Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.605551275, -5.605551275}
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