11X+10=X^2

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Solution for 11X+10=X^2 equation:


Simplifying
11X + 10 = X2

Reorder the terms:
10 + 11X = X2

Solving
10 + 11X = X2

Solving for variable 'X'.

Combine like terms: X2 + -1X2 = 0
10 + 11X + -1X2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-10 + -11X + X2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -11X + 10 + X2 = 0 + 10

Reorder the terms:
-10 + 10 + -11X + X2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -11X + X2 = 0 + 10
-11X + X2 = 0 + 10

Combine like terms: 0 + 10 = 10
-11X + X2 = 10

The X term is -11X.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11X + 30.25 + X2 = 10 + 30.25

Reorder the terms:
30.25 + -11X + X2 = 10 + 30.25

Combine like terms: 10 + 30.25 = 40.25
30.25 + -11X + X2 = 40.25

Factor a perfect square on the left side:
(X + -5.5)(X + -5.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(X + -5.5) equal to 6.34428877 and -6.34428877.

Subproblem 1

X + -5.5 = 6.34428877 Simplifying X + -5.5 = 6.34428877 Reorder the terms: -5.5 + X = 6.34428877 Solving -5.5 + X = 6.34428877 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + X = 6.34428877 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + X = 6.34428877 + 5.5 X = 6.34428877 + 5.5 Combine like terms: 6.34428877 + 5.5 = 11.84428877 X = 11.84428877 Simplifying X = 11.84428877

Subproblem 2

X + -5.5 = -6.34428877 Simplifying X + -5.5 = -6.34428877 Reorder the terms: -5.5 + X = -6.34428877 Solving -5.5 + X = -6.34428877 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + X = -6.34428877 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + X = -6.34428877 + 5.5 X = -6.34428877 + 5.5 Combine like terms: -6.34428877 + 5.5 = -0.84428877 X = -0.84428877 Simplifying X = -0.84428877

Solution

The solution to the problem is based on the solutions from the subproblems. X = {11.84428877, -0.84428877}

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