=25x^2+100x+2500

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Solution for =25x^2+100x+2500 equation: 


Simplifying
0 = 25x2 + 100x + 2500

Reorder the terms:
0 = 2500 + 100x + 25x2

Solving
0 = 2500 + 100x + 25x2

Solving for variable 'x'.

Combine like terms: 0 + -2500 = -2500
-2500 + -100x + -25x2 = 2500 + 100x + 25x2 + -2500 + -100x + -25x2

Reorder the terms:
-2500 + -100x + -25x2 = 2500 + -2500 + 100x + -100x + 25x2 + -25x2

Combine like terms: 2500 + -2500 = 0
-2500 + -100x + -25x2 = 0 + 100x + -100x + 25x2 + -25x2
-2500 + -100x + -25x2 = 100x + -100x + 25x2 + -25x2

Combine like terms: 100x + -100x = 0
-2500 + -100x + -25x2 = 0 + 25x2 + -25x2
-2500 + -100x + -25x2 = 25x2 + -25x2

Combine like terms: 25x2 + -25x2 = 0
-2500 + -100x + -25x2 = 0

Factor out the Greatest Common Factor (GCF), '-25'.
-25(100 + 4x + x2) = 0

Ignore the factor -25.

Subproblem 1
Set the factor '(100 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
100 + 4x + x2 = 0

Solving
100 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + 4x + -100 + x2 = 0 + -100

Reorder the terms:
100 + -100 + 4x + x2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + 4x + x2 = 0 + -100
4x + x2 = 0 + -100

Combine like terms: 0 + -100 = -100
4x + x2 = -100

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -100 + 4

Reorder the terms:
4 + 4x + x2 = -100 + 4

Combine like terms: -100 + 4 = -96
4 + 4x + x2 = -96

Factor a perfect square on the left side:
(x + 2)(x + 2) = -96

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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