8a^2+16a-1=0

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Solution for 8a^2+16a-1=0 equation:


Simplifying
8a2 + 16a + -1 = 0

Reorder the terms:
-1 + 16a + 8a2 = 0

Solving
-1 + 16a + 8a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-0.125 + 2a + a2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 2a + 0.125 + a2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 2a + a2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 2a + a2 = 0 + 0.125
2a + a2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
2a + a2 = 0.125

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 = 0.125 + 1

Reorder the terms:
1 + 2a + a2 = 0.125 + 1

Combine like terms: 0.125 + 1 = 1.125
1 + 2a + a2 = 1.125

Factor a perfect square on the left side:
(a + 1)(a + 1) = 1.125

Calculate the square root of the right side: 1.060660172

Break this problem into two subproblems by setting 
(a + 1) equal to 1.060660172 and -1.060660172.

Subproblem 1

a + 1 = 1.060660172 Simplifying a + 1 = 1.060660172 Reorder the terms: 1 + a = 1.060660172 Solving 1 + a = 1.060660172 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 = 1.060660172 + -1 Combine like terms: 1 + -1 = 0 0 + a = 1.060660172 + -1 a = 1.060660172 + -1 Combine like terms: 1.060660172 + -1 = 0.060660172 a = 0.060660172 Simplifying a = 0.060660172

Subproblem 2

a + 1 = -1.060660172 Simplifying a + 1 = -1.060660172 Reorder the terms: 1 + a = -1.060660172 Solving 1 + a = -1.060660172 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 = -1.060660172 + -1 Combine like terms: 1 + -1 = 0 0 + a = -1.060660172 + -1 a = -1.060660172 + -1 Combine like terms: -1.060660172 + -1 = -2.060660172 a = -2.060660172 Simplifying a = -2.060660172

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.060660172, -2.060660172}

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