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Simplifying a(2a + -8) = 7a + 10 Reorder the terms: a(-8 + 2a) = 7a + 10 (-8 * a + 2a * a) = 7a + 10 (-8a + 2a2) = 7a + 10 Reorder the terms: -8a + 2a2 = 10 + 7a Solving -8a + 2a2 = 10 + 7a Solving for variable 'a'. Reorder the terms: -10 + -8a + -7a + 2a2 = 10 + 7a + -10 + -7a Combine like terms: -8a + -7a = -15a -10 + -15a + 2a2 = 10 + 7a + -10 + -7a Reorder the terms: -10 + -15a + 2a2 = 10 + -10 + 7a + -7a Combine like terms: 10 + -10 = 0 -10 + -15a + 2a2 = 0 + 7a + -7a -10 + -15a + 2a2 = 7a + -7a Combine like terms: 7a + -7a = 0 -10 + -15a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + -7.5a + a2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -7.5a + 5 + a2 = 0 + 5 Reorder the terms: -5 + 5 + -7.5a + a2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -7.5a + a2 = 0 + 5 -7.5a + a2 = 0 + 5 Combine like terms: 0 + 5 = 5 -7.5a + a2 = 5 The a term is -7.5a. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5a + 14.0625 + a2 = 5 + 14.0625 Reorder the terms: 14.0625 + -7.5a + a2 = 5 + 14.0625 Combine like terms: 5 + 14.0625 = 19.0625 14.0625 + -7.5a + a2 = 19.0625 Factor a perfect square on the left side: (a + -3.75)(a + -3.75) = 19.0625 Calculate the square root of the right side: 4.366062299 Break this problem into two subproblems by setting (a + -3.75) equal to 4.366062299 and -4.366062299.Subproblem 1
a + -3.75 = 4.366062299 Simplifying a + -3.75 = 4.366062299 Reorder the terms: -3.75 + a = 4.366062299 Solving -3.75 + a = 4.366062299 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + a = 4.366062299 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + a = 4.366062299 + 3.75 a = 4.366062299 + 3.75 Combine like terms: 4.366062299 + 3.75 = 8.116062299 a = 8.116062299 Simplifying a = 8.116062299Subproblem 2
a + -3.75 = -4.366062299 Simplifying a + -3.75 = -4.366062299 Reorder the terms: -3.75 + a = -4.366062299 Solving -3.75 + a = -4.366062299 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + a = -4.366062299 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + a = -4.366062299 + 3.75 a = -4.366062299 + 3.75 Combine like terms: -4.366062299 + 3.75 = -0.616062299 a = -0.616062299 Simplifying a = -0.616062299Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.116062299, -0.616062299}
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