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Simplifying a2 + -10a + -35 = 0 Reorder the terms: -35 + -10a + a2 = 0 Solving -35 + -10a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -10a + 35 + a2 = 0 + 35 Reorder the terms: -35 + 35 + -10a + a2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -10a + a2 = 0 + 35 -10a + a2 = 0 + 35 Combine like terms: 0 + 35 = 35 -10a + a2 = 35 The a term is -10a. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10a + 25 + a2 = 35 + 25 Reorder the terms: 25 + -10a + a2 = 35 + 25 Combine like terms: 35 + 25 = 60 25 + -10a + a2 = 60 Factor a perfect square on the left side: (a + -5)(a + -5) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (a + -5) equal to 7.745966692 and -7.745966692.Subproblem 1
a + -5 = 7.745966692 Simplifying a + -5 = 7.745966692 Reorder the terms: -5 + a = 7.745966692 Solving -5 + a = 7.745966692 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = 7.745966692 + 5 Combine like terms: -5 + 5 = 0 0 + a = 7.745966692 + 5 a = 7.745966692 + 5 Combine like terms: 7.745966692 + 5 = 12.745966692 a = 12.745966692 Simplifying a = 12.745966692Subproblem 2
a + -5 = -7.745966692 Simplifying a + -5 = -7.745966692 Reorder the terms: -5 + a = -7.745966692 Solving -5 + a = -7.745966692 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + a = -7.745966692 + 5 Combine like terms: -5 + 5 = 0 0 + a = -7.745966692 + 5 a = -7.745966692 + 5 Combine like terms: -7.745966692 + 5 = -2.745966692 a = -2.745966692 Simplifying a = -2.745966692Solution
The solution to the problem is based on the solutions from the subproblems. a = {12.745966692, -2.745966692}
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