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Simplifying 4a2 + -6a + a2 + -12 + 2a + -1 = 0 Reorder the terms: -12 + -1 + -6a + 2a + 4a2 + a2 = 0 Combine like terms: -12 + -1 = -13 -13 + -6a + 2a + 4a2 + a2 = 0 Combine like terms: -6a + 2a = -4a -13 + -4a + 4a2 + a2 = 0 Combine like terms: 4a2 + a2 = 5a2 -13 + -4a + 5a2 = 0 Solving -13 + -4a + 5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + -0.8a + a2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -0.8a + 2.6 + a2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + -0.8a + a2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -0.8a + a2 = 0 + 2.6 -0.8a + a2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 -0.8a + a2 = 2.6 The a term is -0.8a. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8a + 0.16 + a2 = 2.6 + 0.16 Reorder the terms: 0.16 + -0.8a + a2 = 2.6 + 0.16 Combine like terms: 2.6 + 0.16 = 2.76 0.16 + -0.8a + a2 = 2.76 Factor a perfect square on the left side: (a + -0.4)(a + -0.4) = 2.76 Calculate the square root of the right side: 1.661324773 Break this problem into two subproblems by setting (a + -0.4) equal to 1.661324773 and -1.661324773.Subproblem 1
a + -0.4 = 1.661324773 Simplifying a + -0.4 = 1.661324773 Reorder the terms: -0.4 + a = 1.661324773 Solving -0.4 + a = 1.661324773 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + a = 1.661324773 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + a = 1.661324773 + 0.4 a = 1.661324773 + 0.4 Combine like terms: 1.661324773 + 0.4 = 2.061324773 a = 2.061324773 Simplifying a = 2.061324773Subproblem 2
a + -0.4 = -1.661324773 Simplifying a + -0.4 = -1.661324773 Reorder the terms: -0.4 + a = -1.661324773 Solving -0.4 + a = -1.661324773 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + a = -1.661324773 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + a = -1.661324773 + 0.4 a = -1.661324773 + 0.4 Combine like terms: -1.661324773 + 0.4 = -1.261324773 a = -1.261324773 Simplifying a = -1.261324773Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.061324773, -1.261324773}
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