x^2-11x=10

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Solution for x^2-11x=10 equation:


Simplifying
x2 + -11x = 10

Reorder the terms:
-11x + x2 = 10

Solving
-11x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + -11x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -11x + x2 = 0

Begin completing the square.

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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