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Simplifying (a + -4) + 2a(a + -4) + -6a = 0 Reorder the terms: (-4 + a) + 2a(a + -4) + -6a = 0 Remove parenthesis around (-4 + a) -4 + a + 2a(a + -4) + -6a = 0 Reorder the terms: -4 + a + 2a(-4 + a) + -6a = 0 -4 + a + (-4 * 2a + a * 2a) + -6a = 0 -4 + a + (-8a + 2a2) + -6a = 0 Reorder the terms: -4 + a + -8a + -6a + 2a2 = 0 Combine like terms: a + -8a = -7a -4 + -7a + -6a + 2a2 = 0 Combine like terms: -7a + -6a = -13a -4 + -13a + 2a2 = 0 Solving -4 + -13a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -6.5a + a2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -6.5a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + -6.5a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -6.5a + a2 = 0 + 2 -6.5a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 -6.5a + a2 = 2 The a term is -6.5a. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5a + 10.5625 + a2 = 2 + 10.5625 Reorder the terms: 10.5625 + -6.5a + a2 = 2 + 10.5625 Combine like terms: 2 + 10.5625 = 12.5625 10.5625 + -6.5a + a2 = 12.5625 Factor a perfect square on the left side: (a + -3.25)(a + -3.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (a + -3.25) equal to 3.54436172 and -3.54436172.Subproblem 1
a + -3.25 = 3.54436172 Simplifying a + -3.25 = 3.54436172 Reorder the terms: -3.25 + a = 3.54436172 Solving -3.25 + a = 3.54436172 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + a = 3.54436172 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + a = 3.54436172 + 3.25 a = 3.54436172 + 3.25 Combine like terms: 3.54436172 + 3.25 = 6.79436172 a = 6.79436172 Simplifying a = 6.79436172Subproblem 2
a + -3.25 = -3.54436172 Simplifying a + -3.25 = -3.54436172 Reorder the terms: -3.25 + a = -3.54436172 Solving -3.25 + a = -3.54436172 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + a = -3.54436172 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + a = -3.54436172 + 3.25 a = -3.54436172 + 3.25 Combine like terms: -3.54436172 + 3.25 = -0.29436172 a = -0.29436172 Simplifying a = -0.29436172Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.79436172, -0.29436172}
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