3a(2a-25)=180

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Solution for 3a(2a-25)=180 equation:


Simplifying
3a(2a + -25) = 180

Reorder the terms:
3a(-25 + 2a) = 180
(-25 * 3a + 2a * 3a) = 180
(-75a + 6a2) = 180

Solving
-75a + 6a2 = 180

Solving for variable 'a'.

Reorder the terms:
-180 + -75a + 6a2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -75a + 6a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + -25a + 2a2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-60 + -25a + 2a2)' equal to zero and attempt to solve:

Simplifying
-60 + -25a + 2a2 = 0

Solving
-60 + -25a + 2a2 = 0

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

Divide each side by '2'.
-30 + -12.5a + a2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -12.5a + 30 + a2 = 0 + 30

Reorder the terms:
-30 + 30 + -12.5a + a2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -12.5a + a2 = 0 + 30
-12.5a + a2 = 0 + 30

Combine like terms: 0 + 30 = 30
-12.5a + a2 = 30

The a term is -12.5a.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5a + 39.0625 + a2 = 30 + 39.0625

Reorder the terms:
39.0625 + -12.5a + a2 = 30 + 39.0625

Combine like terms: 30 + 39.0625 = 69.0625
39.0625 + -12.5a + a2 = 69.0625

Factor a perfect square on the left side:
(a + -6.25)(a + -6.25) = 69.0625

Calculate the square root of the right side: 8.310385069

Break this problem into two subproblems by setting 
(a + -6.25) equal to 8.310385069 and -8.310385069.


Subproblem 1
a + -6.25 = 8.310385069

Simplifying
a + -6.25 = 8.310385069

Reorder the terms:
-6.25 + a = 8.310385069

Solving
-6.25 + a = 8.310385069

Solving for variable 'a'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + a = 8.310385069 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + a = 8.310385069 + 6.25
a = 8.310385069 + 6.25

Combine like terms: 8.310385069 + 6.25 = 14.560385069
a = 14.560385069

Simplifying
a = 14.560385069


Subproblem 2
a + -6.25 = -8.310385069

Simplifying
a + -6.25 = -8.310385069

Reorder the terms:
-6.25 + a = -8.310385069

Solving
-6.25 + a = -8.310385069

Solving for variable 'a'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + a = -8.310385069 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + a = -8.310385069 + 6.25
a = -8.310385069 + 6.25

Combine like terms: -8.310385069 + 6.25 = -2.060385069
a = -2.060385069

Simplifying
a = -2.060385069


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {14.560385069, -2.060385069}
Solution
a = {14.560385069, -2.060385069}

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