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Simplifying 2a2 + -15a + 12 = 0 Reorder the terms: 12 + -15a + 2a2 = 0 Solving 12 + -15a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6 + -7.5a + a2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -7.5a + -6 + a2 = 0 + -6 Reorder the terms: 6 + -6 + -7.5a + a2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7.5a + a2 = 0 + -6 -7.5a + a2 = 0 + -6 Combine like terms: 0 + -6 = -6 -7.5a + a2 = -6 The a term is -7.5a. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5a + 14.0625 + a2 = -6 + 14.0625 Reorder the terms: 14.0625 + -7.5a + a2 = -6 + 14.0625 Combine like terms: -6 + 14.0625 = 8.0625 14.0625 + -7.5a + a2 = 8.0625 Factor a perfect square on the left side: (a + -3.75)(a + -3.75) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (a + -3.75) equal to 2.839454173 and -2.839454173.Subproblem 1
a + -3.75 = 2.839454173 Simplifying a + -3.75 = 2.839454173 Reorder the terms: -3.75 + a = 2.839454173 Solving -3.75 + a = 2.839454173 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + a = 2.839454173 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + a = 2.839454173 + 3.75 a = 2.839454173 + 3.75 Combine like terms: 2.839454173 + 3.75 = 6.589454173 a = 6.589454173 Simplifying a = 6.589454173Subproblem 2
a + -3.75 = -2.839454173 Simplifying a + -3.75 = -2.839454173 Reorder the terms: -3.75 + a = -2.839454173 Solving -3.75 + a = -2.839454173 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + a = -2.839454173 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + a = -2.839454173 + 3.75 a = -2.839454173 + 3.75 Combine like terms: -2.839454173 + 3.75 = 0.910545827 a = 0.910545827 Simplifying a = 0.910545827Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.589454173, 0.910545827}
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