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Simplifying 6a2 + -15a + -1 = 0 Reorder the terms: -1 + -15a + 6a2 = 0 Solving -1 + -15a + 6a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.1666666667 + -2.5a + a2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -2.5a + 0.1666666667 + a2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -2.5a + a2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -2.5a + a2 = 0 + 0.1666666667 -2.5a + a2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -2.5a + a2 = 0.1666666667 The a term is -2.5a. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5a + 1.5625 + a2 = 0.1666666667 + 1.5625 Reorder the terms: 1.5625 + -2.5a + a2 = 0.1666666667 + 1.5625 Combine like terms: 0.1666666667 + 1.5625 = 1.7291666667 1.5625 + -2.5a + a2 = 1.7291666667 Factor a perfect square on the left side: (a + -1.25)(a + -1.25) = 1.7291666667 Calculate the square root of the right side: 1.31497782 Break this problem into two subproblems by setting (a + -1.25) equal to 1.31497782 and -1.31497782.Subproblem 1
a + -1.25 = 1.31497782 Simplifying a + -1.25 = 1.31497782 Reorder the terms: -1.25 + a = 1.31497782 Solving -1.25 + a = 1.31497782 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + a = 1.31497782 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + a = 1.31497782 + 1.25 a = 1.31497782 + 1.25 Combine like terms: 1.31497782 + 1.25 = 2.56497782 a = 2.56497782 Simplifying a = 2.56497782Subproblem 2
a + -1.25 = -1.31497782 Simplifying a + -1.25 = -1.31497782 Reorder the terms: -1.25 + a = -1.31497782 Solving -1.25 + a = -1.31497782 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + a = -1.31497782 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + a = -1.31497782 + 1.25 a = -1.31497782 + 1.25 Combine like terms: -1.31497782 + 1.25 = -0.06497782 a = -0.06497782 Simplifying a = -0.06497782Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.56497782, -0.06497782}
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