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Simplifying a2 + -8a + -71 = 2 Reorder the terms: -71 + -8a + a2 = 2 Solving -71 + -8a + a2 = 2 Solving for variable 'a'. Reorder the terms: -71 + -2 + -8a + a2 = 2 + -2 Combine like terms: -71 + -2 = -73 -73 + -8a + a2 = 2 + -2 Combine like terms: 2 + -2 = 0 -73 + -8a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '73' to each side of the equation. -73 + -8a + 73 + a2 = 0 + 73 Reorder the terms: -73 + 73 + -8a + a2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + -8a + a2 = 0 + 73 -8a + a2 = 0 + 73 Combine like terms: 0 + 73 = 73 -8a + a2 = 73 The a term is -8a. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8a + 16 + a2 = 73 + 16 Reorder the terms: 16 + -8a + a2 = 73 + 16 Combine like terms: 73 + 16 = 89 16 + -8a + a2 = 89 Factor a perfect square on the left side: (a + -4)(a + -4) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (a + -4) equal to 9.433981132 and -9.433981132.Subproblem 1
a + -4 = 9.433981132 Simplifying a + -4 = 9.433981132 Reorder the terms: -4 + a = 9.433981132 Solving -4 + a = 9.433981132 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = 9.433981132 + 4 Combine like terms: -4 + 4 = 0 0 + a = 9.433981132 + 4 a = 9.433981132 + 4 Combine like terms: 9.433981132 + 4 = 13.433981132 a = 13.433981132 Simplifying a = 13.433981132Subproblem 2
a + -4 = -9.433981132 Simplifying a + -4 = -9.433981132 Reorder the terms: -4 + a = -9.433981132 Solving -4 + a = -9.433981132 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = -9.433981132 + 4 Combine like terms: -4 + 4 = 0 0 + a = -9.433981132 + 4 a = -9.433981132 + 4 Combine like terms: -9.433981132 + 4 = -5.433981132 a = -5.433981132 Simplifying a = -5.433981132Solution
The solution to the problem is based on the solutions from the subproblems. a = {13.433981132, -5.433981132}
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