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Simplifying -6 + -2a + -9a * -9a = 0 Reorder the terms for easier multiplication: -6 + -2a + -9 * -9a * a = 0 Multiply -9 * -9 -6 + -2a + 81a * a = 0 Multiply a * a -6 + -2a + 81a2 = 0 Solving -6 + -2a + 81a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.07407407407 + -0.02469135802a + a2 = 0 Move the constant term to the right: Add '0.07407407407' to each side of the equation. -0.07407407407 + -0.02469135802a + 0.07407407407 + a2 = 0 + 0.07407407407 Reorder the terms: -0.07407407407 + 0.07407407407 + -0.02469135802a + a2 = 0 + 0.07407407407 Combine like terms: -0.07407407407 + 0.07407407407 = 0.00000000000 0.00000000000 + -0.02469135802a + a2 = 0 + 0.07407407407 -0.02469135802a + a2 = 0 + 0.07407407407 Combine like terms: 0 + 0.07407407407 = 0.07407407407 -0.02469135802a + a2 = 0.07407407407 The a term is -0.02469135802a. Take half its coefficient (-0.01234567901). Square it (0.0001524157902) and add it to both sides. Add '0.0001524157902' to each side of the equation. -0.02469135802a + 0.0001524157902 + a2 = 0.07407407407 + 0.0001524157902 Reorder the terms: 0.0001524157902 + -0.02469135802a + a2 = 0.07407407407 + 0.0001524157902 Combine like terms: 0.07407407407 + 0.0001524157902 = 0.0742264898602 0.0001524157902 + -0.02469135802a + a2 = 0.0742264898602 Factor a perfect square on the left side: (a + -0.01234567901)(a + -0.01234567901) = 0.0742264898602 Calculate the square root of the right side: 0.272445389 Break this problem into two subproblems by setting (a + -0.01234567901) equal to 0.272445389 and -0.272445389.Subproblem 1
a + -0.01234567901 = 0.272445389 Simplifying a + -0.01234567901 = 0.272445389 Reorder the terms: -0.01234567901 + a = 0.272445389 Solving -0.01234567901 + a = 0.272445389 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.01234567901' to each side of the equation. -0.01234567901 + 0.01234567901 + a = 0.272445389 + 0.01234567901 Combine like terms: -0.01234567901 + 0.01234567901 = 0.00000000000 0.00000000000 + a = 0.272445389 + 0.01234567901 a = 0.272445389 + 0.01234567901 Combine like terms: 0.272445389 + 0.01234567901 = 0.28479106801 a = 0.28479106801 Simplifying a = 0.28479106801Subproblem 2
a + -0.01234567901 = -0.272445389 Simplifying a + -0.01234567901 = -0.272445389 Reorder the terms: -0.01234567901 + a = -0.272445389 Solving -0.01234567901 + a = -0.272445389 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.01234567901' to each side of the equation. -0.01234567901 + 0.01234567901 + a = -0.272445389 + 0.01234567901 Combine like terms: -0.01234567901 + 0.01234567901 = 0.00000000000 0.00000000000 + a = -0.272445389 + 0.01234567901 a = -0.272445389 + 0.01234567901 Combine like terms: -0.272445389 + 0.01234567901 = -0.26009970999 a = -0.26009970999 Simplifying a = -0.26009970999Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.28479106801, -0.26009970999}
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