10x^2-400x+2304=0

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Solution for 10x^2-400x+2304=0 equation: 


Simplifying
10x2 + -400x + 2304 = 0

Reorder the terms:
2304 + -400x + 10x2 = 0

Solving
2304 + -400x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1152 + -200x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1152 + -200x + 5x2)' equal to zero and attempt to solve:

Simplifying
1152 + -200x + 5x2 = 0

Solving
1152 + -200x + 5x2 = 0

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

Divide each side by '5'.
230.4 + -40x + x2 = 0

Move the constant term to the right:

Add '-230.4' to each side of the equation.
230.4 + -40x + -230.4 + x2 = 0 + -230.4

Reorder the terms:
230.4 + -230.4 + -40x + x2 = 0 + -230.4

Combine like terms: 230.4 + -230.4 = 0.0
0.0 + -40x + x2 = 0 + -230.4
-40x + x2 = 0 + -230.4

Combine like terms: 0 + -230.4 = -230.4
-40x + x2 = -230.4

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = -230.4 + 400

Reorder the terms:
400 + -40x + x2 = -230.4 + 400

Combine like terms: -230.4 + 400 = 169.6
400 + -40x + x2 = 169.6

Factor a perfect square on the left side:
(x + -20)(x + -20) = 169.6

Calculate the square root of the right side: 13.023056477

Break this problem into two subproblems by setting 
(x + -20) equal to 13.023056477 and -13.023056477.


Subproblem 1
x + -20 = 13.023056477

Simplifying
x + -20 = 13.023056477

Reorder the terms:
-20 + x = 13.023056477

Solving
-20 + x = 13.023056477

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = 13.023056477 + 20

Combine like terms: -20 + 20 = 0
0 + x = 13.023056477 + 20
x = 13.023056477 + 20

Combine like terms: 13.023056477 + 20 = 33.023056477
x = 33.023056477

Simplifying
x = 33.023056477


Subproblem 2
x + -20 = -13.023056477

Simplifying
x + -20 = -13.023056477

Reorder the terms:
-20 + x = -13.023056477

Solving
-20 + x = -13.023056477

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = -13.023056477 + 20

Combine like terms: -20 + 20 = 0
0 + x = -13.023056477 + 20
x = -13.023056477 + 20

Combine like terms: -13.023056477 + 20 = 6.976943523
x = 6.976943523

Simplifying
x = 6.976943523


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {33.023056477, 6.976943523}
Solution
x = {33.023056477, 6.976943523}

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