8*a^2+a-1.68=0

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Solution for 8*a^2+a-1.68=0 equation:


Simplifying
8a2 + a + -1.68 = 0

Reorder the terms:
-1.68 + a + 8a2 = 0

Solving
-1.68 + a + 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'.
-0.21 + 0.125a + a2 = 0

Move the constant term to the right:

Add '0.21' to each side of the equation.
-0.21 + 0.125a + 0.21 + a2 = 0 + 0.21

Reorder the terms:
-0.21 + 0.21 + 0.125a + a2 = 0 + 0.21

Combine like terms: -0.21 + 0.21 = 0.00
0.00 + 0.125a + a2 = 0 + 0.21
0.125a + a2 = 0 + 0.21

Combine like terms: 0 + 0.21 = 0.21
0.125a + a2 = 0.21

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.125a + 0.25 + a2 = 0.21 + 0.25

Reorder the terms:
0.25 + 0.125a + a2 = 0.21 + 0.25

Combine like terms: 0.21 + 0.25 = 0.46
0.25 + 0.125a + a2 = 0.46

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 0.46

Calculate the square root of the right side: 0.678232998

Break this problem into two subproblems by setting 
(a + 0.5) equal to 0.678232998 and -0.678232998.

Subproblem 1

a + 0.5 = 0.678232998 Simplifying a + 0.5 = 0.678232998 Reorder the terms: 0.5 + a = 0.678232998 Solving 0.5 + a = 0.678232998 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 0.678232998 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 0.678232998 + -0.5 a = 0.678232998 + -0.5 Combine like terms: 0.678232998 + -0.5 = 0.178232998 a = 0.178232998 Simplifying a = 0.178232998

Subproblem 2

a + 0.5 = -0.678232998 Simplifying a + 0.5 = -0.678232998 Reorder the terms: 0.5 + a = -0.678232998 Solving 0.5 + a = -0.678232998 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -0.678232998 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -0.678232998 + -0.5 a = -0.678232998 + -0.5 Combine like terms: -0.678232998 + -0.5 = -1.178232998 a = -1.178232998 Simplifying a = -1.178232998

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.178232998, -1.178232998}

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