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Simplifying a(a + -8) + -3(a + -2) = 0 Reorder the terms: a(-8 + a) + -3(a + -2) = 0 (-8 * a + a * a) + -3(a + -2) = 0 (-8a + a2) + -3(a + -2) = 0 Reorder the terms: -8a + a2 + -3(-2 + a) = 0 -8a + a2 + (-2 * -3 + a * -3) = 0 -8a + a2 + (6 + -3a) = 0 Reorder the terms: 6 + -8a + -3a + a2 = 0 Combine like terms: -8a + -3a = -11a 6 + -11a + a2 = 0 Solving 6 + -11a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -11a + -6 + a2 = 0 + -6 Reorder the terms: 6 + -6 + -11a + a2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -11a + a2 = 0 + -6 -11a + a2 = 0 + -6 Combine like terms: 0 + -6 = -6 -11a + a2 = -6 The a term is -11a. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11a + 30.25 + a2 = -6 + 30.25 Reorder the terms: 30.25 + -11a + a2 = -6 + 30.25 Combine like terms: -6 + 30.25 = 24.25 30.25 + -11a + a2 = 24.25 Factor a perfect square on the left side: (a + -5.5)(a + -5.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (a + -5.5) equal to 4.924428901 and -4.924428901.Subproblem 1
a + -5.5 = 4.924428901 Simplifying a + -5.5 = 4.924428901 Reorder the terms: -5.5 + a = 4.924428901 Solving -5.5 + a = 4.924428901 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + a = 4.924428901 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + a = 4.924428901 + 5.5 a = 4.924428901 + 5.5 Combine like terms: 4.924428901 + 5.5 = 10.424428901 a = 10.424428901 Simplifying a = 10.424428901Subproblem 2
a + -5.5 = -4.924428901 Simplifying a + -5.5 = -4.924428901 Reorder the terms: -5.5 + a = -4.924428901 Solving -5.5 + a = -4.924428901 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + a = -4.924428901 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + a = -4.924428901 + 5.5 a = -4.924428901 + 5.5 Combine like terms: -4.924428901 + 5.5 = 0.575571099 a = 0.575571099 Simplifying a = 0.575571099Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.424428901, 0.575571099}
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