6x^2+300x+5625=0

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Solution for 6x^2+300x+5625=0 equation: 


Simplifying
6x2 + 300x + 5625 = 0

Reorder the terms:
5625 + 300x + 6x2 = 0

Solving
5625 + 300x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1875 + 100x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(1875 + 100x + 2x2)' equal to zero and attempt to solve:

Simplifying
1875 + 100x + 2x2 = 0

Solving
1875 + 100x + 2x2 = 0

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

Divide each side by '2'.
937.5 + 50x + x2 = 0

Move the constant term to the right:

Add '-937.5' to each side of the equation.
937.5 + 50x + -937.5 + x2 = 0 + -937.5

Reorder the terms:
937.5 + -937.5 + 50x + x2 = 0 + -937.5

Combine like terms: 937.5 + -937.5 = 0.0
0.0 + 50x + x2 = 0 + -937.5
50x + x2 = 0 + -937.5

Combine like terms: 0 + -937.5 = -937.5
50x + x2 = -937.5

The x term is 50x.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50x + 625 + x2 = -937.5 + 625

Reorder the terms:
625 + 50x + x2 = -937.5 + 625

Combine like terms: -937.5 + 625 = -312.5
625 + 50x + x2 = -312.5

Factor a perfect square on the left side:
(x + 25)(x + 25) = -312.5

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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