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Simplifying 8a2 + -16a + -12 = -5 Reorder the terms: -12 + -16a + 8a2 = -5 Solving -12 + -16a + 8a2 = -5 Solving for variable 'a'. Reorder the terms: -12 + 5 + -16a + 8a2 = -5 + 5 Combine like terms: -12 + 5 = -7 -7 + -16a + 8a2 = -5 + 5 Combine like terms: -5 + 5 = 0 -7 + -16a + 8a2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + -2a + a2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -2a + 0.875 + a2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -2a + a2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -2a + a2 = 0 + 0.875 -2a + a2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -2a + a2 = 0.875 The a term is -2a. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2a + 1 + a2 = 0.875 + 1 Reorder the terms: 1 + -2a + a2 = 0.875 + 1 Combine like terms: 0.875 + 1 = 1.875 1 + -2a + a2 = 1.875 Factor a perfect square on the left side: (a + -1)(a + -1) = 1.875 Calculate the square root of the right side: 1.369306394 Break this problem into two subproblems by setting (a + -1) equal to 1.369306394 and -1.369306394.Subproblem 1
a + -1 = 1.369306394 Simplifying a + -1 = 1.369306394 Reorder the terms: -1 + a = 1.369306394 Solving -1 + a = 1.369306394 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 1.369306394 + 1 Combine like terms: -1 + 1 = 0 0 + a = 1.369306394 + 1 a = 1.369306394 + 1 Combine like terms: 1.369306394 + 1 = 2.369306394 a = 2.369306394 Simplifying a = 2.369306394Subproblem 2
a + -1 = -1.369306394 Simplifying a + -1 = -1.369306394 Reorder the terms: -1 + a = -1.369306394 Solving -1 + a = -1.369306394 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = -1.369306394 + 1 Combine like terms: -1 + 1 = 0 0 + a = -1.369306394 + 1 a = -1.369306394 + 1 Combine like terms: -1.369306394 + 1 = -0.369306394 a = -0.369306394 Simplifying a = -0.369306394Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.369306394, -0.369306394}
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