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Simplifying a2 + -3a = 3a + 25 Reorder the terms: -3a + a2 = 3a + 25 Reorder the terms: -3a + a2 = 25 + 3a Solving -3a + a2 = 25 + 3a Solving for variable 'a'. Reorder the terms: -25 + -3a + -3a + a2 = 25 + 3a + -25 + -3a Combine like terms: -3a + -3a = -6a -25 + -6a + a2 = 25 + 3a + -25 + -3a Reorder the terms: -25 + -6a + a2 = 25 + -25 + 3a + -3a Combine like terms: 25 + -25 = 0 -25 + -6a + a2 = 0 + 3a + -3a -25 + -6a + a2 = 3a + -3a Combine like terms: 3a + -3a = 0 -25 + -6a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -6a + 25 + a2 = 0 + 25 Reorder the terms: -25 + 25 + -6a + a2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -6a + a2 = 0 + 25 -6a + a2 = 0 + 25 Combine like terms: 0 + 25 = 25 -6a + a2 = 25 The a term is -6a. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6a + 9 + a2 = 25 + 9 Reorder the terms: 9 + -6a + a2 = 25 + 9 Combine like terms: 25 + 9 = 34 9 + -6a + a2 = 34 Factor a perfect square on the left side: (a + -3)(a + -3) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (a + -3) equal to 5.830951895 and -5.830951895.Subproblem 1
a + -3 = 5.830951895 Simplifying a + -3 = 5.830951895 Reorder the terms: -3 + a = 5.830951895 Solving -3 + a = 5.830951895 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 5.830951895 + 3 Combine like terms: -3 + 3 = 0 0 + a = 5.830951895 + 3 a = 5.830951895 + 3 Combine like terms: 5.830951895 + 3 = 8.830951895 a = 8.830951895 Simplifying a = 8.830951895Subproblem 2
a + -3 = -5.830951895 Simplifying a + -3 = -5.830951895 Reorder the terms: -3 + a = -5.830951895 Solving -3 + a = -5.830951895 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -5.830951895 + 3 Combine like terms: -3 + 3 = 0 0 + a = -5.830951895 + 3 a = -5.830951895 + 3 Combine like terms: -5.830951895 + 3 = -2.830951895 a = -2.830951895 Simplifying a = -2.830951895Solution
The solution to the problem is based on the solutions from the subproblems. a = {8.830951895, -2.830951895}
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