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Simplifying a2 + -2a + -43 = 0 Reorder the terms: -43 + -2a + a2 = 0 Solving -43 + -2a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -2a + 43 + a2 = 0 + 43 Reorder the terms: -43 + 43 + -2a + a2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -2a + a2 = 0 + 43 -2a + a2 = 0 + 43 Combine like terms: 0 + 43 = 43 -2a + a2 = 43 The a term is -2a. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2a + 1 + a2 = 43 + 1 Reorder the terms: 1 + -2a + a2 = 43 + 1 Combine like terms: 43 + 1 = 44 1 + -2a + a2 = 44 Factor a perfect square on the left side: (a + -1)(a + -1) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (a + -1) equal to 6.633249581 and -6.633249581.Subproblem 1
a + -1 = 6.633249581 Simplifying a + -1 = 6.633249581 Reorder the terms: -1 + a = 6.633249581 Solving -1 + a = 6.633249581 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 6.633249581 + 1 Combine like terms: -1 + 1 = 0 0 + a = 6.633249581 + 1 a = 6.633249581 + 1 Combine like terms: 6.633249581 + 1 = 7.633249581 a = 7.633249581 Simplifying a = 7.633249581Subproblem 2
a + -1 = -6.633249581 Simplifying a + -1 = -6.633249581 Reorder the terms: -1 + a = -6.633249581 Solving -1 + a = -6.633249581 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = -6.633249581 + 1 Combine like terms: -1 + 1 = 0 0 + a = -6.633249581 + 1 a = -6.633249581 + 1 Combine like terms: -6.633249581 + 1 = -5.633249581 a = -5.633249581 Simplifying a = -5.633249581Solution
The solution to the problem is based on the solutions from the subproblems. a = {7.633249581, -5.633249581}
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