25+X+10X=3X^2

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Solution for 25+X+10X=3X^2 equation: 


Simplifying
25 + X + 10X = 3X2

Combine like terms: X + 10X = 11X
25 + 11X = 3X2

Solving
25 + 11X = 3X2

Solving for variable 'X'.

Combine like terms: 3X2 + -3X2 = 0
25 + 11X + -3X2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-8.333333333 + -3.666666667X + X2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + -3.666666667X + 8.333333333 + X2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + -3.666666667X + X2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + -3.666666667X + X2 = 0 + 8.333333333
-3.666666667X + X2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
-3.666666667X + X2 = 8.333333333

The X term is -3.666666667X.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667X + 3.361111114 + X2 = 8.333333333 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667X + X2 = 8.333333333 + 3.361111114

Combine like terms: 8.333333333 + 3.361111114 = 11.694444447
3.361111114 + -3.666666667X + X2 = 11.694444447

Factor a perfect square on the left side:
(X + -1.833333334)(X + -1.833333334) = 11.694444447

Calculate the square root of the right side: 3.419714088

Break this problem into two subproblems by setting 
(X + -1.833333334) equal to 3.419714088 and -3.419714088.


Subproblem 1
X + -1.833333334 = 3.419714088

Simplifying
X + -1.833333334 = 3.419714088

Reorder the terms:
-1.833333334 + X = 3.419714088

Solving
-1.833333334 + X = 3.419714088

Solving for variable 'X'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + X = 3.419714088 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + X = 3.419714088 + 1.833333334
X = 3.419714088 + 1.833333334

Combine like terms: 3.419714088 + 1.833333334 = 5.253047422
X = 5.253047422

Simplifying
X = 5.253047422


Subproblem 2
X + -1.833333334 = -3.419714088

Simplifying
X + -1.833333334 = -3.419714088

Reorder the terms:
-1.833333334 + X = -3.419714088

Solving
-1.833333334 + X = -3.419714088

Solving for variable 'X'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + X = -3.419714088 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + X = -3.419714088 + 1.833333334
X = -3.419714088 + 1.833333334

Combine like terms: -3.419714088 + 1.833333334 = -1.586380754
X = -1.586380754

Simplifying
X = -1.586380754


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {5.253047422, -1.586380754}

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