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Simplifying 2a + 6 + -1a2 = 3 + -3a Reorder the terms: 6 + 2a + -1a2 = 3 + -3a Solving 6 + 2a + -1a2 = 3 + -3a Solving for variable 'a'. Reorder the terms: 6 + -3 + 2a + 3a + -1a2 = 3 + -3a + -3 + 3a Combine like terms: 6 + -3 = 3 3 + 2a + 3a + -1a2 = 3 + -3a + -3 + 3a Combine like terms: 2a + 3a = 5a 3 + 5a + -1a2 = 3 + -3a + -3 + 3a Reorder the terms: 3 + 5a + -1a2 = 3 + -3 + -3a + 3a Combine like terms: 3 + -3 = 0 3 + 5a + -1a2 = 0 + -3a + 3a 3 + 5a + -1a2 = -3a + 3a Combine like terms: -3a + 3a = 0 3 + 5a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -5a + a2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -5a + 3 + a2 = 0 + 3 Reorder the terms: -3 + 3 + -5a + a2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5a + a2 = 0 + 3 -5a + a2 = 0 + 3 Combine like terms: 0 + 3 = 3 -5a + a2 = 3 The a term is -5a. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5a + 6.25 + a2 = 3 + 6.25 Reorder the terms: 6.25 + -5a + a2 = 3 + 6.25 Combine like terms: 3 + 6.25 = 9.25 6.25 + -5a + a2 = 9.25 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (a + -2.5) equal to 3.041381265 and -3.041381265.Subproblem 1
a + -2.5 = 3.041381265 Simplifying a + -2.5 = 3.041381265 Reorder the terms: -2.5 + a = 3.041381265 Solving -2.5 + a = 3.041381265 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = 3.041381265 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 3.041381265 + 2.5 a = 3.041381265 + 2.5 Combine like terms: 3.041381265 + 2.5 = 5.541381265 a = 5.541381265 Simplifying a = 5.541381265Subproblem 2
a + -2.5 = -3.041381265 Simplifying a + -2.5 = -3.041381265 Reorder the terms: -2.5 + a = -3.041381265 Solving -2.5 + a = -3.041381265 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = -3.041381265 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -3.041381265 + 2.5 a = -3.041381265 + 2.5 Combine like terms: -3.041381265 + 2.5 = -0.541381265 a = -0.541381265 Simplifying a = -0.541381265Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.541381265, -0.541381265}
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