4x^2-210x+1450=0

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Solution for 4x^2-210x+1450=0 equation: 


Simplifying
4x2 + -210x + 1450 = 0

Reorder the terms:
1450 + -210x + 4x2 = 0

Solving
1450 + -210x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(725 + -105x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(725 + -105x + 2x2)' equal to zero and attempt to solve:

Simplifying
725 + -105x + 2x2 = 0

Solving
725 + -105x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
362.5 + -52.5x + x2 = 0

Move the constant term to the right:

Add '-362.5' to each side of the equation.
362.5 + -52.5x + -362.5 + x2 = 0 + -362.5

Reorder the terms:
362.5 + -362.5 + -52.5x + x2 = 0 + -362.5

Combine like terms: 362.5 + -362.5 = 0.0
0.0 + -52.5x + x2 = 0 + -362.5
-52.5x + x2 = 0 + -362.5

Combine like terms: 0 + -362.5 = -362.5
-52.5x + x2 = -362.5

The x term is -52.5x.  Take half its coefficient (-26.25).
Square it (689.0625) and add it to both sides.

Add '689.0625' to each side of the equation.
-52.5x + 689.0625 + x2 = -362.5 + 689.0625

Reorder the terms:
689.0625 + -52.5x + x2 = -362.5 + 689.0625

Combine like terms: -362.5 + 689.0625 = 326.5625
689.0625 + -52.5x + x2 = 326.5625

Factor a perfect square on the left side:
(x + -26.25)(x + -26.25) = 326.5625

Calculate the square root of the right side: 18.071040369

Break this problem into two subproblems by setting 
(x + -26.25) equal to 18.071040369 and -18.071040369.


Subproblem 1
x + -26.25 = 18.071040369

Simplifying
x + -26.25 = 18.071040369

Reorder the terms:
-26.25 + x = 18.071040369

Solving
-26.25 + x = 18.071040369

Solving for variable 'x'.

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

Add '26.25' to each side of the equation.
-26.25 + 26.25 + x = 18.071040369 + 26.25

Combine like terms: -26.25 + 26.25 = 0.00
0.00 + x = 18.071040369 + 26.25
x = 18.071040369 + 26.25

Combine like terms: 18.071040369 + 26.25 = 44.321040369
x = 44.321040369

Simplifying
x = 44.321040369


Subproblem 2
x + -26.25 = -18.071040369

Simplifying
x + -26.25 = -18.071040369

Reorder the terms:
-26.25 + x = -18.071040369

Solving
-26.25 + x = -18.071040369

Solving for variable 'x'.

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

Add '26.25' to each side of the equation.
-26.25 + 26.25 + x = -18.071040369 + 26.25

Combine like terms: -26.25 + 26.25 = 0.00
0.00 + x = -18.071040369 + 26.25
x = -18.071040369 + 26.25

Combine like terms: -18.071040369 + 26.25 = 8.178959631
x = 8.178959631

Simplifying
x = 8.178959631


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {44.321040369, 8.178959631}
Solution
x = {44.321040369, 8.178959631}

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