10x^2-295x+1825=0

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Solution for 10x^2-295x+1825=0 equation: 


Simplifying
10x2 + -295x + 1825 = 0

Reorder the terms:
1825 + -295x + 10x2 = 0

Solving
1825 + -295x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(365 + -59x + 2x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(365 + -59x + 2x2)' equal to zero and attempt to solve:

Simplifying
365 + -59x + 2x2 = 0

Solving
365 + -59x + 2x2 = 0

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

Divide each side by '2'.
182.5 + -29.5x + x2 = 0

Move the constant term to the right:

Add '-182.5' to each side of the equation.
182.5 + -29.5x + -182.5 + x2 = 0 + -182.5

Reorder the terms:
182.5 + -182.5 + -29.5x + x2 = 0 + -182.5

Combine like terms: 182.5 + -182.5 = 0.0
0.0 + -29.5x + x2 = 0 + -182.5
-29.5x + x2 = 0 + -182.5

Combine like terms: 0 + -182.5 = -182.5
-29.5x + x2 = -182.5

The x term is -29.5x.  Take half its coefficient (-14.75).
Square it (217.5625) and add it to both sides.

Add '217.5625' to each side of the equation.
-29.5x + 217.5625 + x2 = -182.5 + 217.5625

Reorder the terms:
217.5625 + -29.5x + x2 = -182.5 + 217.5625

Combine like terms: -182.5 + 217.5625 = 35.0625
217.5625 + -29.5x + x2 = 35.0625

Factor a perfect square on the left side:
(x + -14.75)(x + -14.75) = 35.0625

Calculate the square root of the right side: 5.921359641

Break this problem into two subproblems by setting 
(x + -14.75) equal to 5.921359641 and -5.921359641.


Subproblem 1
x + -14.75 = 5.921359641

Simplifying
x + -14.75 = 5.921359641

Reorder the terms:
-14.75 + x = 5.921359641

Solving
-14.75 + x = 5.921359641

Solving for variable 'x'.

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

Add '14.75' to each side of the equation.
-14.75 + 14.75 + x = 5.921359641 + 14.75

Combine like terms: -14.75 + 14.75 = 0.00
0.00 + x = 5.921359641 + 14.75
x = 5.921359641 + 14.75

Combine like terms: 5.921359641 + 14.75 = 20.671359641
x = 20.671359641

Simplifying
x = 20.671359641


Subproblem 2
x + -14.75 = -5.921359641

Simplifying
x + -14.75 = -5.921359641

Reorder the terms:
-14.75 + x = -5.921359641

Solving
-14.75 + x = -5.921359641

Solving for variable 'x'.

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

Add '14.75' to each side of the equation.
-14.75 + 14.75 + x = -5.921359641 + 14.75

Combine like terms: -14.75 + 14.75 = 0.00
0.00 + x = -5.921359641 + 14.75
x = -5.921359641 + 14.75

Combine like terms: -5.921359641 + 14.75 = 8.828640359
x = 8.828640359

Simplifying
x = 8.828640359


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.671359641, 8.828640359}
Solution
x = {20.671359641, 8.828640359}

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