2x^2-4x-420=0

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Solution for 2x^2-4x-420=0 equation: 


Simplifying
2x2 + -4x + -420 = 0

Reorder the terms:
-420 + -4x + 2x2 = 0

Solving
-420 + -4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-210 + -2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-210 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-210 + -2x + x2 = 0

Solving
-210 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '210' to each side of the equation.
-210 + -2x + 210 + x2 = 0 + 210

Reorder the terms:
-210 + 210 + -2x + x2 = 0 + 210

Combine like terms: -210 + 210 = 0
0 + -2x + x2 = 0 + 210
-2x + x2 = 0 + 210

Combine like terms: 0 + 210 = 210
-2x + x2 = 210

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 210 + 1

Reorder the terms:
1 + -2x + x2 = 210 + 1

Combine like terms: 210 + 1 = 211
1 + -2x + x2 = 211

Factor a perfect square on the left side:
(x + -1)(x + -1) = 211

Calculate the square root of the right side: 14.525839046

Break this problem into two subproblems by setting 
(x + -1) equal to 14.525839046 and -14.525839046.


Subproblem 1
x + -1 = 14.525839046

Simplifying
x + -1 = 14.525839046

Reorder the terms:
-1 + x = 14.525839046

Solving
-1 + x = 14.525839046

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 14.525839046 + 1

Combine like terms: -1 + 1 = 0
0 + x = 14.525839046 + 1
x = 14.525839046 + 1

Combine like terms: 14.525839046 + 1 = 15.525839046
x = 15.525839046

Simplifying
x = 15.525839046


Subproblem 2
x + -1 = -14.525839046

Simplifying
x + -1 = -14.525839046

Reorder the terms:
-1 + x = -14.525839046

Solving
-1 + x = -14.525839046

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -14.525839046 + 1

Combine like terms: -1 + 1 = 0
0 + x = -14.525839046 + 1
x = -14.525839046 + 1

Combine like terms: -14.525839046 + 1 = -13.525839046
x = -13.525839046

Simplifying
x = -13.525839046


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.525839046, -13.525839046}
Solution
x = {15.525839046, -13.525839046}

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