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Simplifying a2 = 5.2a + -6 Reorder the terms: a2 = -6 + 5.2a Solving a2 = -6 + 5.2a Solving for variable 'a'. Reorder the terms: 6 + -5.2a + a2 = -6 + 5.2a + 6 + -5.2a Reorder the terms: 6 + -5.2a + a2 = -6 + 6 + 5.2a + -5.2a Combine like terms: -6 + 6 = 0 6 + -5.2a + a2 = 0 + 5.2a + -5.2a 6 + -5.2a + a2 = 5.2a + -5.2a Combine like terms: 5.2a + -5.2a = 0.0 6 + -5.2a + a2 = 0.0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -5.2a + -6 + a2 = 0.0 + -6 Reorder the terms: 6 + -6 + -5.2a + a2 = 0.0 + -6 Combine like terms: 6 + -6 = 0 0 + -5.2a + a2 = 0.0 + -6 -5.2a + a2 = 0.0 + -6 Combine like terms: 0.0 + -6 = -6 -5.2a + a2 = -6 The a term is -5.2a. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2a + 6.76 + a2 = -6 + 6.76 Reorder the terms: 6.76 + -5.2a + a2 = -6 + 6.76 Combine like terms: -6 + 6.76 = 0.76 6.76 + -5.2a + a2 = 0.76 Factor a perfect square on the left side: (a + -2.6)(a + -2.6) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (a + -2.6) equal to 0.871779789 and -0.871779789.Subproblem 1
a + -2.6 = 0.871779789 Simplifying a + -2.6 = 0.871779789 Reorder the terms: -2.6 + a = 0.871779789 Solving -2.6 + a = 0.871779789 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + a = 0.871779789 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + a = 0.871779789 + 2.6 a = 0.871779789 + 2.6 Combine like terms: 0.871779789 + 2.6 = 3.471779789 a = 3.471779789 Simplifying a = 3.471779789Subproblem 2
a + -2.6 = -0.871779789 Simplifying a + -2.6 = -0.871779789 Reorder the terms: -2.6 + a = -0.871779789 Solving -2.6 + a = -0.871779789 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + a = -0.871779789 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + a = -0.871779789 + 2.6 a = -0.871779789 + 2.6 Combine like terms: -0.871779789 + 2.6 = 1.728220211 a = 1.728220211 Simplifying a = 1.728220211Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.471779789, 1.728220211}
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