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Simplifying (4a2 + -3a + 4) + -1(3a2 + -7a + 6) = 0 Reorder the terms: (4 + -3a + 4a2) + -1(3a2 + -7a + 6) = 0 Remove parenthesis around (4 + -3a + 4a2) 4 + -3a + 4a2 + -1(3a2 + -7a + 6) = 0 Reorder the terms: 4 + -3a + 4a2 + -1(6 + -7a + 3a2) = 0 4 + -3a + 4a2 + (6 * -1 + -7a * -1 + 3a2 * -1) = 0 4 + -3a + 4a2 + (-6 + 7a + -3a2) = 0 Reorder the terms: 4 + -6 + -3a + 7a + 4a2 + -3a2 = 0 Combine like terms: 4 + -6 = -2 -2 + -3a + 7a + 4a2 + -3a2 = 0 Combine like terms: -3a + 7a = 4a -2 + 4a + 4a2 + -3a2 = 0 Combine like terms: 4a2 + -3a2 = 1a2 -2 + 4a + 1a2 = 0 Solving -2 + 4a + 1a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 4a + 2 + a2 = 0 + 2 Reorder the terms: -2 + 2 + 4a + a2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4a + a2 = 0 + 2 4a + a2 = 0 + 2 Combine like terms: 0 + 2 = 2 4a + a2 = 2 The a term is 4a. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4a + 4 + a2 = 2 + 4 Reorder the terms: 4 + 4a + a2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + 4a + a2 = 6 Factor a perfect square on the left side: (a + 2)(a + 2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (a + 2) equal to 2.449489743 and -2.449489743.Subproblem 1
a + 2 = 2.449489743 Simplifying a + 2 = 2.449489743 Reorder the terms: 2 + a = 2.449489743 Solving 2 + a = 2.449489743 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + a = 2.449489743 + -2 a = 2.449489743 + -2 Combine like terms: 2.449489743 + -2 = 0.449489743 a = 0.449489743 Simplifying a = 0.449489743Subproblem 2
a + 2 = -2.449489743 Simplifying a + 2 = -2.449489743 Reorder the terms: 2 + a = -2.449489743 Solving 2 + a = -2.449489743 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = -2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + a = -2.449489743 + -2 a = -2.449489743 + -2 Combine like terms: -2.449489743 + -2 = -4.449489743 a = -4.449489743 Simplifying a = -4.449489743Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.449489743, -4.449489743}
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