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Simplifying 2a + 11 = a(a + -3) Reorder the terms: 11 + 2a = a(a + -3) Reorder the terms: 11 + 2a = a(-3 + a) 11 + 2a = (-3 * a + a * a) 11 + 2a = (-3a + a2) Solving 11 + 2a = -3a + a2 Solving for variable 'a'. Combine like terms: 2a + 3a = 5a 11 + 5a + -1a2 = -3a + a2 + 3a + -1a2 Reorder the terms: 11 + 5a + -1a2 = -3a + 3a + a2 + -1a2 Combine like terms: -3a + 3a = 0 11 + 5a + -1a2 = 0 + a2 + -1a2 11 + 5a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 11 + 5a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + -5a + a2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -5a + 11 + a2 = 0 + 11 Reorder the terms: -11 + 11 + -5a + a2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -5a + a2 = 0 + 11 -5a + a2 = 0 + 11 Combine like terms: 0 + 11 = 11 -5a + a2 = 11 The a term is -5a. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5a + 6.25 + a2 = 11 + 6.25 Reorder the terms: 6.25 + -5a + a2 = 11 + 6.25 Combine like terms: 11 + 6.25 = 17.25 6.25 + -5a + a2 = 17.25 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (a + -2.5) equal to 4.153311931 and -4.153311931.Subproblem 1
a + -2.5 = 4.153311931 Simplifying a + -2.5 = 4.153311931 Reorder the terms: -2.5 + a = 4.153311931 Solving -2.5 + a = 4.153311931 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = 4.153311931 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 4.153311931 + 2.5 a = 4.153311931 + 2.5 Combine like terms: 4.153311931 + 2.5 = 6.653311931 a = 6.653311931 Simplifying a = 6.653311931Subproblem 2
a + -2.5 = -4.153311931 Simplifying a + -2.5 = -4.153311931 Reorder the terms: -2.5 + a = -4.153311931 Solving -2.5 + a = -4.153311931 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = -4.153311931 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -4.153311931 + 2.5 a = -4.153311931 + 2.5 Combine like terms: -4.153311931 + 2.5 = -1.653311931 a = -1.653311931 Simplifying a = -1.653311931Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.653311931, -1.653311931}
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