4x^2+420x+1700=0

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Solution for 4x^2+420x+1700=0 equation: 


Simplifying
4x2 + 420x + 1700 = 0

Reorder the terms:
1700 + 420x + 4x2 = 0

Solving
1700 + 420x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(425 + 105x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(425 + 105x + x2)' equal to zero and attempt to solve:

Simplifying
425 + 105x + x2 = 0

Solving
425 + 105x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-425' to each side of the equation.
425 + 105x + -425 + x2 = 0 + -425

Reorder the terms:
425 + -425 + 105x + x2 = 0 + -425

Combine like terms: 425 + -425 = 0
0 + 105x + x2 = 0 + -425
105x + x2 = 0 + -425

Combine like terms: 0 + -425 = -425
105x + x2 = -425

The x term is 105x.  Take half its coefficient (52.5).
Square it (2756.25) and add it to both sides.

Add '2756.25' to each side of the equation.
105x + 2756.25 + x2 = -425 + 2756.25

Reorder the terms:
2756.25 + 105x + x2 = -425 + 2756.25

Combine like terms: -425 + 2756.25 = 2331.25
2756.25 + 105x + x2 = 2331.25

Factor a perfect square on the left side:
(x + 52.5)(x + 52.5) = 2331.25

Calculate the square root of the right side: 48.28301979

Break this problem into two subproblems by setting 
(x + 52.5) equal to 48.28301979 and -48.28301979.


Subproblem 1
x + 52.5 = 48.28301979

Simplifying
x + 52.5 = 48.28301979

Reorder the terms:
52.5 + x = 48.28301979

Solving
52.5 + x = 48.28301979

Solving for variable 'x'.

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

Add '-52.5' to each side of the equation.
52.5 + -52.5 + x = 48.28301979 + -52.5

Combine like terms: 52.5 + -52.5 = 0.0
0.0 + x = 48.28301979 + -52.5
x = 48.28301979 + -52.5

Combine like terms: 48.28301979 + -52.5 = -4.21698021
x = -4.21698021

Simplifying
x = -4.21698021


Subproblem 2
x + 52.5 = -48.28301979

Simplifying
x + 52.5 = -48.28301979

Reorder the terms:
52.5 + x = -48.28301979

Solving
52.5 + x = -48.28301979

Solving for variable 'x'.

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

Add '-52.5' to each side of the equation.
52.5 + -52.5 + x = -48.28301979 + -52.5

Combine like terms: 52.5 + -52.5 = 0.0
0.0 + x = -48.28301979 + -52.5
x = -48.28301979 + -52.5

Combine like terms: -48.28301979 + -52.5 = -100.78301979
x = -100.78301979

Simplifying
x = -100.78301979


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.21698021, -100.78301979}
Solution
x = {-4.21698021, -100.78301979}

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