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Simplifying (a + -3)(a + -2) = 4 Reorder the terms: (-3 + a)(a + -2) = 4 Reorder the terms: (-3 + a)(-2 + a) = 4 Multiply (-3 + a) * (-2 + a) (-3(-2 + a) + a(-2 + a)) = 4 ((-2 * -3 + a * -3) + a(-2 + a)) = 4 ((6 + -3a) + a(-2 + a)) = 4 (6 + -3a + (-2 * a + a * a)) = 4 (6 + -3a + (-2a + a2)) = 4 Combine like terms: -3a + -2a = -5a (6 + -5a + a2) = 4 Solving 6 + -5a + a2 = 4 Solving for variable 'a'. Reorder the terms: 6 + -4 + -5a + a2 = 4 + -4 Combine like terms: 6 + -4 = 2 2 + -5a + a2 = 4 + -4 Combine like terms: 4 + -4 = 0 2 + -5a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -5a + -2 + a2 = 0 + -2 Reorder the terms: 2 + -2 + -5a + a2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5a + a2 = 0 + -2 -5a + a2 = 0 + -2 Combine like terms: 0 + -2 = -2 -5a + a2 = -2 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 = -2 + 6.25 Reorder the terms: 6.25 + -5a + a2 = -2 + 6.25 Combine like terms: -2 + 6.25 = 4.25 6.25 + -5a + a2 = 4.25 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (a + -2.5) equal to 2.061552813 and -2.061552813.Subproblem 1
a + -2.5 = 2.061552813 Simplifying a + -2.5 = 2.061552813 Reorder the terms: -2.5 + a = 2.061552813 Solving -2.5 + a = 2.061552813 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 = 2.061552813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 2.061552813 + 2.5 a = 2.061552813 + 2.5 Combine like terms: 2.061552813 + 2.5 = 4.561552813 a = 4.561552813 Simplifying a = 4.561552813Subproblem 2
a + -2.5 = -2.061552813 Simplifying a + -2.5 = -2.061552813 Reorder the terms: -2.5 + a = -2.061552813 Solving -2.5 + a = -2.061552813 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 = -2.061552813 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -2.061552813 + 2.5 a = -2.061552813 + 2.5 Combine like terms: -2.061552813 + 2.5 = 0.438447187 a = 0.438447187 Simplifying a = 0.438447187Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.561552813, 0.438447187}
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