a(5-a)-6(a+4)=

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Solution for a(5-a)-6(a+4)= equation:


Simplifying
a(5 + -1a) + -6(a + 4) = 0
(5 * a + -1a * a) + -6(a + 4) = 0
(5a + -1a2) + -6(a + 4) = 0

Reorder the terms:
5a + -1a2 + -6(4 + a) = 0
5a + -1a2 + (4 * -6 + a * -6) = 0
5a + -1a2 + (-24 + -6a) = 0

Reorder the terms:
-24 + 5a + -6a + -1a2 = 0

Combine like terms: 5a + -6a = -1a
-24 + -1a + -1a2 = 0

Solving
-24 + -1a + -1a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(24 + a + a2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(24 + a + a2)' equal to zero and attempt to solve:

Simplifying
24 + a + a2 = 0

Solving
24 + a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + a + -24 + a2 = 0 + -24

Reorder the terms:
24 + -24 + a + a2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + a + a2 = 0 + -24
a + a2 = 0 + -24

Combine like terms: 0 + -24 = -24
a + a2 = -24

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.
a + 0.25 + a2 = -24 + 0.25

Reorder the terms:
0.25 + a + a2 = -24 + 0.25

Combine like terms: -24 + 0.25 = -23.75
0.25 + a + a2 = -23.75

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = -23.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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