5*x*x-410x+300=300x

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Solution for 5*x*x-410x+300=300x equation: 


Simplifying
5x * x + -410x + 300 = 300x

Multiply x * x
5x2 + -410x + 300 = 300x

Reorder the terms:
300 + -410x + 5x2 = 300x

Solving
300 + -410x + 5x2 = 300x

Solving for variable 'x'.

Reorder the terms:
300 + -410x + -300x + 5x2 = 300x + -300x

Combine like terms: -410x + -300x = -710x
300 + -710x + 5x2 = 300x + -300x

Combine like terms: 300x + -300x = 0
300 + -710x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(60 + -142x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(60 + -142x + x2)' equal to zero and attempt to solve:

Simplifying
60 + -142x + x2 = 0

Solving
60 + -142x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-60' to each side of the equation.
60 + -142x + -60 + x2 = 0 + -60

Reorder the terms:
60 + -60 + -142x + x2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -142x + x2 = 0 + -60
-142x + x2 = 0 + -60

Combine like terms: 0 + -60 = -60
-142x + x2 = -60

The x term is -142x.  Take half its coefficient (-71).
Square it (5041) and add it to both sides.

Add '5041' to each side of the equation.
-142x + 5041 + x2 = -60 + 5041

Reorder the terms:
5041 + -142x + x2 = -60 + 5041

Combine like terms: -60 + 5041 = 4981
5041 + -142x + x2 = 4981

Factor a perfect square on the left side:
(x + -71)(x + -71) = 4981

Calculate the square root of the right side: 70.576199954

Break this problem into two subproblems by setting 
(x + -71) equal to 70.576199954 and -70.576199954.


Subproblem 1
x + -71 = 70.576199954

Simplifying
x + -71 = 70.576199954

Reorder the terms:
-71 + x = 70.576199954

Solving
-71 + x = 70.576199954

Solving for variable 'x'.

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

Add '71' to each side of the equation.
-71 + 71 + x = 70.576199954 + 71

Combine like terms: -71 + 71 = 0
0 + x = 70.576199954 + 71
x = 70.576199954 + 71

Combine like terms: 70.576199954 + 71 = 141.576199954
x = 141.576199954

Simplifying
x = 141.576199954


Subproblem 2
x + -71 = -70.576199954

Simplifying
x + -71 = -70.576199954

Reorder the terms:
-71 + x = -70.576199954

Solving
-71 + x = -70.576199954

Solving for variable 'x'.

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

Add '71' to each side of the equation.
-71 + 71 + x = -70.576199954 + 71

Combine like terms: -71 + 71 = 0
0 + x = -70.576199954 + 71
x = -70.576199954 + 71

Combine like terms: -70.576199954 + 71 = 0.423800046
x = 0.423800046

Simplifying
x = 0.423800046


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {141.576199954, 0.423800046}
Solution
x = {141.576199954, 0.423800046}

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