4a^2-8a-11=0

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Solution for 4a^2-8a-11=0 equation:


Simplifying
4a2 + -8a + -11 = 0

Reorder the terms:
-11 + -8a + 4a2 = 0

Solving
-11 + -8a + 4a2 = 0

Solving for variable 'a'.

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

Divide each side by '4'.
-2.75 + -2a + a2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + -2a + 2.75 + a2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + -2a + a2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + -2a + a2 = 0 + 2.75
-2a + a2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
-2a + a2 = 2.75

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 = 2.75 + 1

Reorder the terms:
1 + -2a + a2 = 2.75 + 1

Combine like terms: 2.75 + 1 = 3.75
1 + -2a + a2 = 3.75

Factor a perfect square on the left side:
(a + -1)(a + -1) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
(a + -1) equal to 1.936491673 and -1.936491673.

Subproblem 1

a + -1 = 1.936491673 Simplifying a + -1 = 1.936491673 Reorder the terms: -1 + a = 1.936491673 Solving -1 + a = 1.936491673 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 = 1.936491673 + 1 Combine like terms: -1 + 1 = 0 0 + a = 1.936491673 + 1 a = 1.936491673 + 1 Combine like terms: 1.936491673 + 1 = 2.936491673 a = 2.936491673 Simplifying a = 2.936491673

Subproblem 2

a + -1 = -1.936491673 Simplifying a + -1 = -1.936491673 Reorder the terms: -1 + a = -1.936491673 Solving -1 + a = -1.936491673 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 = -1.936491673 + 1 Combine like terms: -1 + 1 = 0 0 + a = -1.936491673 + 1 a = -1.936491673 + 1 Combine like terms: -1.936491673 + 1 = -0.936491673 a = -0.936491673 Simplifying a = -0.936491673

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.936491673, -0.936491673}

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