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Simplifying 3a2 + 6a + -73 = 3 Reorder the terms: -73 + 6a + 3a2 = 3 Solving -73 + 6a + 3a2 = 3 Solving for variable 'a'. Reorder the terms: -73 + -3 + 6a + 3a2 = 3 + -3 Combine like terms: -73 + -3 = -76 -76 + 6a + 3a2 = 3 + -3 Combine like terms: 3 + -3 = 0 -76 + 6a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -25.33333333 + 2a + a2 = 0 Move the constant term to the right: Add '25.33333333' to each side of the equation. -25.33333333 + 2a + 25.33333333 + a2 = 0 + 25.33333333 Reorder the terms: -25.33333333 + 25.33333333 + 2a + a2 = 0 + 25.33333333 Combine like terms: -25.33333333 + 25.33333333 = 0.00000000 0.00000000 + 2a + a2 = 0 + 25.33333333 2a + a2 = 0 + 25.33333333 Combine like terms: 0 + 25.33333333 = 25.33333333 2a + a2 = 25.33333333 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 = 25.33333333 + 1 Reorder the terms: 1 + 2a + a2 = 25.33333333 + 1 Combine like terms: 25.33333333 + 1 = 26.33333333 1 + 2a + a2 = 26.33333333 Factor a perfect square on the left side: (a + 1)(a + 1) = 26.33333333 Calculate the square root of the right side: 5.131601439 Break this problem into two subproblems by setting (a + 1) equal to 5.131601439 and -5.131601439.Subproblem 1
a + 1 = 5.131601439 Simplifying a + 1 = 5.131601439 Reorder the terms: 1 + a = 5.131601439 Solving 1 + a = 5.131601439 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 = 5.131601439 + -1 Combine like terms: 1 + -1 = 0 0 + a = 5.131601439 + -1 a = 5.131601439 + -1 Combine like terms: 5.131601439 + -1 = 4.131601439 a = 4.131601439 Simplifying a = 4.131601439Subproblem 2
a + 1 = -5.131601439 Simplifying a + 1 = -5.131601439 Reorder the terms: 1 + a = -5.131601439 Solving 1 + a = -5.131601439 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 = -5.131601439 + -1 Combine like terms: 1 + -1 = 0 0 + a = -5.131601439 + -1 a = -5.131601439 + -1 Combine like terms: -5.131601439 + -1 = -6.131601439 a = -6.131601439 Simplifying a = -6.131601439Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.131601439, -6.131601439}
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