2X(X+7)+5X(2X-8)=(10X^2)-3X+11

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Solution for 2X(X+7)+5X(2X-8)=(10X^2)-3X+11 equation: 


Simplifying
2X(X + 7) + 5X(2X + -8) = (10X2) + -3X + 11

Reorder the terms:
2X(7 + X) + 5X(2X + -8) = (10X2) + -3X + 11
(7 * 2X + X * 2X) + 5X(2X + -8) = (10X2) + -3X + 11
(14X + 2X2) + 5X(2X + -8) = (10X2) + -3X + 11

Reorder the terms:
14X + 2X2 + 5X(-8 + 2X) = (10X2) + -3X + 11
14X + 2X2 + (-8 * 5X + 2X * 5X) = (10X2) + -3X + 11
14X + 2X2 + (-40X + 10X2) = (10X2) + -3X + 11

Reorder the terms:
14X + -40X + 2X2 + 10X2 = (10X2) + -3X + 11

Combine like terms: 14X + -40X = -26X
-26X + 2X2 + 10X2 = (10X2) + -3X + 11

Combine like terms: 2X2 + 10X2 = 12X2
-26X + 12X2 = (10X2) + -3X + 11

Reorder the terms:
-26X + 12X2 = 11 + -3X + (10X2)

Solving
-26X + 12X2 = 11 + -3X + (10X2)

Solving for variable 'X'.

Reorder the terms:
-11 + -26X + 3X + 12X2 + (-10X2) = 11 + -3X + (10X2) + -11 + 3X + (-10X2)

Combine like terms: -26X + 3X = -23X
-11 + -23X + 12X2 + (-10X2) = 11 + -3X + (10X2) + -11 + 3X + (-10X2)

Combine like terms: 12X2 + (-10X2) = 2X2
-11 + -23X + 2X2 = 11 + -3X + (10X2) + -11 + 3X + (-10X2)

Reorder the terms:
-11 + -23X + 2X2 = 11 + -11 + -3X + 3X + (10X2) + (-10X2)

Combine like terms: 11 + -11 = 0
-11 + -23X + 2X2 = 0 + -3X + 3X + (10X2) + (-10X2)
-11 + -23X + 2X2 = -3X + 3X + (10X2) + (-10X2)

Combine like terms: -3X + 3X = 0
-11 + -23X + 2X2 = 0 + (10X2) + (-10X2)
-11 + -23X + 2X2 = (10X2) + (-10X2)

Combine like terms: (10X2) + (-10X2) = 0
-11 + -23X + 2X2 = 0

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

Divide each side by '2'.
-5.5 + -11.5X + X2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -11.5X + 5.5 + X2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -11.5X + X2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -11.5X + X2 = 0 + 5.5
-11.5X + X2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-11.5X + X2 = 5.5

The X term is -11.5X.  Take half its coefficient (-5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
-11.5X + 33.0625 + X2 = 5.5 + 33.0625

Reorder the terms:
33.0625 + -11.5X + X2 = 5.5 + 33.0625

Combine like terms: 5.5 + 33.0625 = 38.5625
33.0625 + -11.5X + X2 = 38.5625

Factor a perfect square on the left side:
(X + -5.75)(X + -5.75) = 38.5625

Calculate the square root of the right side: 6.209871174

Break this problem into two subproblems by setting 
(X + -5.75) equal to 6.209871174 and -6.209871174.


Subproblem 1
X + -5.75 = 6.209871174

Simplifying
X + -5.75 = 6.209871174

Reorder the terms:
-5.75 + X = 6.209871174

Solving
-5.75 + X = 6.209871174

Solving for variable 'X'.

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

Add '5.75' to each side of the equation.
-5.75 + 5.75 + X = 6.209871174 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + X = 6.209871174 + 5.75
X = 6.209871174 + 5.75

Combine like terms: 6.209871174 + 5.75 = 11.959871174
X = 11.959871174

Simplifying
X = 11.959871174


Subproblem 2
X + -5.75 = -6.209871174

Simplifying
X + -5.75 = -6.209871174

Reorder the terms:
-5.75 + X = -6.209871174

Solving
-5.75 + X = -6.209871174

Solving for variable 'X'.

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

Add '5.75' to each side of the equation.
-5.75 + 5.75 + X = -6.209871174 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + X = -6.209871174 + 5.75
X = -6.209871174 + 5.75

Combine like terms: -6.209871174 + 5.75 = -0.459871174
X = -0.459871174

Simplifying
X = -0.459871174


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {11.959871174, -0.459871174}

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