2a^2-11a-3=0

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Solution for 2a^2-11a-3=0 equation:


Simplifying
2a2 + -11a + -3 = 0

Reorder the terms:
-3 + -11a + 2a2 = 0

Solving
-3 + -11a + 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'.
-1.5 + -5.5a + a2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -5.5a + 1.5 + a2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -5.5a + a2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -5.5a + a2 = 0 + 1.5
-5.5a + a2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-5.5a + a2 = 1.5

The a term is -5.5a.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5a + 7.5625 + a2 = 1.5 + 7.5625

Reorder the terms:
7.5625 + -5.5a + a2 = 1.5 + 7.5625

Combine like terms: 1.5 + 7.5625 = 9.0625
7.5625 + -5.5a + a2 = 9.0625

Factor a perfect square on the left side:
(a + -2.75)(a + -2.75) = 9.0625

Calculate the square root of the right side: 3.010398645

Break this problem into two subproblems by setting 
(a + -2.75) equal to 3.010398645 and -3.010398645.

Subproblem 1

a + -2.75 = 3.010398645 Simplifying a + -2.75 = 3.010398645 Reorder the terms: -2.75 + a = 3.010398645 Solving -2.75 + a = 3.010398645 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + a = 3.010398645 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + a = 3.010398645 + 2.75 a = 3.010398645 + 2.75 Combine like terms: 3.010398645 + 2.75 = 5.760398645 a = 5.760398645 Simplifying a = 5.760398645

Subproblem 2

a + -2.75 = -3.010398645 Simplifying a + -2.75 = -3.010398645 Reorder the terms: -2.75 + a = -3.010398645 Solving -2.75 + a = -3.010398645 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + a = -3.010398645 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + a = -3.010398645 + 2.75 a = -3.010398645 + 2.75 Combine like terms: -3.010398645 + 2.75 = -0.260398645 a = -0.260398645 Simplifying a = -0.260398645

Solution

The solution to the problem is based on the solutions from the subproblems. a = {5.760398645, -0.260398645}

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