2a^2+6a-1=0

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Solution for 2a^2+6a-1=0 equation:


Simplifying
2a2 + 6a + -1 = 0

Reorder the terms:
-1 + 6a + 2a2 = 0

Solving
-1 + 6a + 2a2 = 0

Solving for variable 'a'.

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

Divide each side by '2'.
-0.5 + 3a + a2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 3a + 0.5 + a2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 3a + a2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 3a + a2 = 0 + 0.5
3a + a2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
3a + a2 = 0.5

The a term is 3a.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3a + 2.25 + a2 = 0.5 + 2.25

Reorder the terms:
2.25 + 3a + a2 = 0.5 + 2.25

Combine like terms: 0.5 + 2.25 = 2.75
2.25 + 3a + a2 = 2.75

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(a + 1.5) equal to 1.658312395 and -1.658312395.

Subproblem 1

a + 1.5 = 1.658312395 Simplifying a + 1.5 = 1.658312395 Reorder the terms: 1.5 + a = 1.658312395 Solving 1.5 + a = 1.658312395 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = 1.658312395 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 1.658312395 + -1.5 a = 1.658312395 + -1.5 Combine like terms: 1.658312395 + -1.5 = 0.158312395 a = 0.158312395 Simplifying a = 0.158312395

Subproblem 2

a + 1.5 = -1.658312395 Simplifying a + 1.5 = -1.658312395 Reorder the terms: 1.5 + a = -1.658312395 Solving 1.5 + a = -1.658312395 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = -1.658312395 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -1.658312395 + -1.5 a = -1.658312395 + -1.5 Combine like terms: -1.658312395 + -1.5 = -3.158312395 a = -3.158312395 Simplifying a = -3.158312395

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.158312395, -3.158312395}

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