5x^2-600x+1600=0

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Solution for 5x^2-600x+1600=0 equation:


Simplifying
5x2 + -600x + 1600 = 0

Reorder the terms:
1600 + -600x + 5x2 = 0

Solving
1600 + -600x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(320 + -120x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(320 + -120x + x2)' equal to zero and attempt to solve:

Simplifying
320 + -120x + x2 = 0

Solving
320 + -120x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-320' to each side of the equation.
320 + -120x + -320 + x2 = 0 + -320

Reorder the terms:
320 + -320 + -120x + x2 = 0 + -320

Combine like terms: 320 + -320 = 0
0 + -120x + x2 = 0 + -320
-120x + x2 = 0 + -320

Combine like terms: 0 + -320 = -320
-120x + x2 = -320

The x term is -120x.  Take half its coefficient (-60).
Square it (3600) and add it to both sides.

Add '3600' to each side of the equation.
-120x + 3600 + x2 = -320 + 3600

Reorder the terms:
3600 + -120x + x2 = -320 + 3600

Combine like terms: -320 + 3600 = 3280
3600 + -120x + x2 = 3280

Factor a perfect square on the left side:
(x + -60)(x + -60) = 3280

Calculate the square root of the right side: 57.271284253

Break this problem into two subproblems by setting 
(x + -60) equal to 57.271284253 and -57.271284253.


Subproblem 1
x + -60 = 57.271284253

Simplifying
x + -60 = 57.271284253

Reorder the terms:
-60 + x = 57.271284253

Solving
-60 + x = 57.271284253

Solving for variable 'x'.

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

Add '60' to each side of the equation.
-60 + 60 + x = 57.271284253 + 60

Combine like terms: -60 + 60 = 0
0 + x = 57.271284253 + 60
x = 57.271284253 + 60

Combine like terms: 57.271284253 + 60 = 117.271284253
x = 117.271284253

Simplifying
x = 117.271284253


Subproblem 2
x + -60 = -57.271284253

Simplifying
x + -60 = -57.271284253

Reorder the terms:
-60 + x = -57.271284253

Solving
-60 + x = -57.271284253

Solving for variable 'x'.

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

Add '60' to each side of the equation.
-60 + 60 + x = -57.271284253 + 60

Combine like terms: -60 + 60 = 0
0 + x = -57.271284253 + 60
x = -57.271284253 + 60

Combine like terms: -57.271284253 + 60 = 2.728715747
x = 2.728715747

Simplifying
x = 2.728715747


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {117.271284253, 2.728715747}
Solution
x = {117.271284253, 2.728715747}

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