10x^2-298x+200=0

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Solution for 10x^2-298x+200=0 equation: 


Simplifying
10x2 + -298x + 200 = 0

Reorder the terms:
200 + -298x + 10x2 = 0

Solving
200 + -298x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(100 + -149x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(100 + -149x + 5x2)' equal to zero and attempt to solve:

Simplifying
100 + -149x + 5x2 = 0

Solving
100 + -149x + 5x2 = 0

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

Divide each side by '5'.
20 + -29.8x + x2 = 0

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -29.8x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -29.8x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -29.8x + x2 = 0 + -20
-29.8x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-29.8x + x2 = -20

The x term is -29.8x.  Take half its coefficient (-14.9).
Square it (222.01) and add it to both sides.

Add '222.01' to each side of the equation.
-29.8x + 222.01 + x2 = -20 + 222.01

Reorder the terms:
222.01 + -29.8x + x2 = -20 + 222.01

Combine like terms: -20 + 222.01 = 202.01
222.01 + -29.8x + x2 = 202.01

Factor a perfect square on the left side:
(x + -14.9)(x + -14.9) = 202.01

Calculate the square root of the right side: 14.213022198

Break this problem into two subproblems by setting 
(x + -14.9) equal to 14.213022198 and -14.213022198.


Subproblem 1
x + -14.9 = 14.213022198

Simplifying
x + -14.9 = 14.213022198

Reorder the terms:
-14.9 + x = 14.213022198

Solving
-14.9 + x = 14.213022198

Solving for variable 'x'.

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

Add '14.9' to each side of the equation.
-14.9 + 14.9 + x = 14.213022198 + 14.9

Combine like terms: -14.9 + 14.9 = 0.0
0.0 + x = 14.213022198 + 14.9
x = 14.213022198 + 14.9

Combine like terms: 14.213022198 + 14.9 = 29.113022198
x = 29.113022198

Simplifying
x = 29.113022198


Subproblem 2
x + -14.9 = -14.213022198

Simplifying
x + -14.9 = -14.213022198

Reorder the terms:
-14.9 + x = -14.213022198

Solving
-14.9 + x = -14.213022198

Solving for variable 'x'.

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

Add '14.9' to each side of the equation.
-14.9 + 14.9 + x = -14.213022198 + 14.9

Combine like terms: -14.9 + 14.9 = 0.0
0.0 + x = -14.213022198 + 14.9
x = -14.213022198 + 14.9

Combine like terms: -14.213022198 + 14.9 = 0.686977802
x = 0.686977802

Simplifying
x = 0.686977802


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.113022198, 0.686977802}
Solution
x = {29.113022198, 0.686977802}

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