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Simplifying 4a2 + 9a + -1 = 0 Reorder the terms: -1 + 9a + 4a2 = 0 Solving -1 + 9a + 4a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + 2.25a + a2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 2.25a + 0.25 + a2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 2.25a + a2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 2.25a + a2 = 0 + 0.25 2.25a + a2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 2.25a + a2 = 0.25 The a term is 2.25a. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25a + 1.265625 + a2 = 0.25 + 1.265625 Reorder the terms: 1.265625 + 2.25a + a2 = 0.25 + 1.265625 Combine like terms: 0.25 + 1.265625 = 1.515625 1.265625 + 2.25a + a2 = 1.515625 Factor a perfect square on the left side: (a + 1.125)(a + 1.125) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (a + 1.125) equal to 1.231107225 and -1.231107225.Subproblem 1
a + 1.125 = 1.231107225 Simplifying a + 1.125 = 1.231107225 Reorder the terms: 1.125 + a = 1.231107225 Solving 1.125 + a = 1.231107225 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + a = 1.231107225 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + a = 1.231107225 + -1.125 a = 1.231107225 + -1.125 Combine like terms: 1.231107225 + -1.125 = 0.106107225 a = 0.106107225 Simplifying a = 0.106107225Subproblem 2
a + 1.125 = -1.231107225 Simplifying a + 1.125 = -1.231107225 Reorder the terms: 1.125 + a = -1.231107225 Solving 1.125 + a = -1.231107225 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + a = -1.231107225 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + a = -1.231107225 + -1.125 a = -1.231107225 + -1.125 Combine like terms: -1.231107225 + -1.125 = -2.356107225 a = -2.356107225 Simplifying a = -2.356107225Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.106107225, -2.356107225}
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