4a^2-100a-240=0

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Solution for 4a^2-100a-240=0 equation: 


Simplifying
4a2 + -100a + -240 = 0

Reorder the terms:
-240 + -100a + 4a2 = 0

Solving
-240 + -100a + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-60 + -25a + a2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-60 + -25a + a2)' equal to zero and attempt to solve:

Simplifying
-60 + -25a + a2 = 0

Solving
-60 + -25a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + -25a + 60 + a2 = 0 + 60

Reorder the terms:
-60 + 60 + -25a + a2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -25a + a2 = 0 + 60
-25a + a2 = 0 + 60

Combine like terms: 0 + 60 = 60
-25a + a2 = 60

The a term is -25a.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25a + 156.25 + a2 = 60 + 156.25

Reorder the terms:
156.25 + -25a + a2 = 60 + 156.25

Combine like terms: 60 + 156.25 = 216.25
156.25 + -25a + a2 = 216.25

Factor a perfect square on the left side:
(a + -12.5)(a + -12.5) = 216.25

Calculate the square root of the right side: 14.70544117

Break this problem into two subproblems by setting 
(a + -12.5) equal to 14.70544117 and -14.70544117.


Subproblem 1
a + -12.5 = 14.70544117

Simplifying
a + -12.5 = 14.70544117

Reorder the terms:
-12.5 + a = 14.70544117

Solving
-12.5 + a = 14.70544117

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '12.5' to each side of the equation.
-12.5 + 12.5 + a = 14.70544117 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + a = 14.70544117 + 12.5
a = 14.70544117 + 12.5

Combine like terms: 14.70544117 + 12.5 = 27.20544117
a = 27.20544117

Simplifying
a = 27.20544117


Subproblem 2
a + -12.5 = -14.70544117

Simplifying
a + -12.5 = -14.70544117

Reorder the terms:
-12.5 + a = -14.70544117

Solving
-12.5 + a = -14.70544117

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '12.5' to each side of the equation.
-12.5 + 12.5 + a = -14.70544117 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + a = -14.70544117 + 12.5
a = -14.70544117 + 12.5

Combine like terms: -14.70544117 + 12.5 = -2.20544117
a = -2.20544117

Simplifying
a = -2.20544117


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {27.20544117, -2.20544117}
Solution
a = {27.20544117, -2.20544117}

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