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Simplifying 8a(a) + 10a = -11a + 4 Multiply a * a 8a2 + 10a = -11a + 4 Reorder the terms: 10a + 8a2 = -11a + 4 Reorder the terms: 10a + 8a2 = 4 + -11a Solving 10a + 8a2 = 4 + -11a Solving for variable 'a'. Reorder the terms: -4 + 10a + 11a + 8a2 = 4 + -11a + -4 + 11a Combine like terms: 10a + 11a = 21a -4 + 21a + 8a2 = 4 + -11a + -4 + 11a Reorder the terms: -4 + 21a + 8a2 = 4 + -4 + -11a + 11a Combine like terms: 4 + -4 = 0 -4 + 21a + 8a2 = 0 + -11a + 11a -4 + 21a + 8a2 = -11a + 11a Combine like terms: -11a + 11a = 0 -4 + 21a + 8a2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.5 + 2.625a + a2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 2.625a + 0.5 + a2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 2.625a + a2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 2.625a + a2 = 0 + 0.5 2.625a + a2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 2.625a + a2 = 0.5 The a term is 2.625a. Take half its coefficient (1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. 2.625a + 1.72265625 + a2 = 0.5 + 1.72265625 Reorder the terms: 1.72265625 + 2.625a + a2 = 0.5 + 1.72265625 Combine like terms: 0.5 + 1.72265625 = 2.22265625 1.72265625 + 2.625a + a2 = 2.22265625 Factor a perfect square on the left side: (a + 1.3125)(a + 1.3125) = 2.22265625 Calculate the square root of the right side: 1.490857555 Break this problem into two subproblems by setting (a + 1.3125) equal to 1.490857555 and -1.490857555.Subproblem 1
a + 1.3125 = 1.490857555 Simplifying a + 1.3125 = 1.490857555 Reorder the terms: 1.3125 + a = 1.490857555 Solving 1.3125 + a = 1.490857555 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.3125' to each side of the equation. 1.3125 + -1.3125 + a = 1.490857555 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + a = 1.490857555 + -1.3125 a = 1.490857555 + -1.3125 Combine like terms: 1.490857555 + -1.3125 = 0.178357555 a = 0.178357555 Simplifying a = 0.178357555Subproblem 2
a + 1.3125 = -1.490857555 Simplifying a + 1.3125 = -1.490857555 Reorder the terms: 1.3125 + a = -1.490857555 Solving 1.3125 + a = -1.490857555 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.3125' to each side of the equation. 1.3125 + -1.3125 + a = -1.490857555 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + a = -1.490857555 + -1.3125 a = -1.490857555 + -1.3125 Combine like terms: -1.490857555 + -1.3125 = -2.803357555 a = -2.803357555 Simplifying a = -2.803357555Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.178357555, -2.803357555}
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