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Simplifying 9a2 + 4 + -24a = 0 Reorder the terms: 4 + -24a + 9a2 = 0 Solving 4 + -24a + 9a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.4444444444 + -2.666666667a + a2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -2.666666667a + -0.4444444444 + a2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -2.666666667a + a2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -2.666666667a + a2 = 0 + -0.4444444444 -2.666666667a + a2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -2.666666667a + a2 = -0.4444444444 The a term is -2.666666667a. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667a + 1.777777780 + a2 = -0.4444444444 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667a + a2 = -0.4444444444 + 1.777777780 Combine like terms: -0.4444444444 + 1.777777780 = 1.3333333356 1.777777780 + -2.666666667a + a2 = 1.3333333356 Factor a perfect square on the left side: (a + -1.333333334)(a + -1.333333334) = 1.3333333356 Calculate the square root of the right side: 1.154700539 Break this problem into two subproblems by setting (a + -1.333333334) equal to 1.154700539 and -1.154700539.Subproblem 1
a + -1.333333334 = 1.154700539 Simplifying a + -1.333333334 = 1.154700539 Reorder the terms: -1.333333334 + a = 1.154700539 Solving -1.333333334 + a = 1.154700539 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + a = 1.154700539 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + a = 1.154700539 + 1.333333334 a = 1.154700539 + 1.333333334 Combine like terms: 1.154700539 + 1.333333334 = 2.488033873 a = 2.488033873 Simplifying a = 2.488033873Subproblem 2
a + -1.333333334 = -1.154700539 Simplifying a + -1.333333334 = -1.154700539 Reorder the terms: -1.333333334 + a = -1.154700539 Solving -1.333333334 + a = -1.154700539 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + a = -1.154700539 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + a = -1.154700539 + 1.333333334 a = -1.154700539 + 1.333333334 Combine like terms: -1.154700539 + 1.333333334 = 0.178632795 a = 0.178632795 Simplifying a = 0.178632795Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.488033873, 0.178632795}
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