x*x+x-1=10

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Solution for x*x+x-1=10 equation: 


Simplifying
x * x + x + -1 = 10

Multiply x * x
x2 + x + -1 = 10

Reorder the terms:
-1 + x + x2 = 10

Solving
-1 + x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-1 + -10 + x + x2 = 10 + -10

Combine like terms: -1 + -10 = -11
-11 + x + x2 = 10 + -10

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

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + x + x2 = 0 + 11

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 11 + 0.25

Reorder the terms:
0.25 + x + x2 = 11 + 0.25

Combine like terms: 11 + 0.25 = 11.25
0.25 + x + x2 = 11.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.354101966 and -3.354101966.


Subproblem 1
x + 0.5 = 3.354101966

Simplifying
x + 0.5 = 3.354101966

Reorder the terms:
0.5 + x = 3.354101966

Solving
0.5 + x = 3.354101966

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 3.354101966 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.354101966 + -0.5
x = 3.354101966 + -0.5

Combine like terms: 3.354101966 + -0.5 = 2.854101966
x = 2.854101966

Simplifying
x = 2.854101966


Subproblem 2
x + 0.5 = -3.354101966

Simplifying
x + 0.5 = -3.354101966

Reorder the terms:
0.5 + x = -3.354101966

Solving
0.5 + x = -3.354101966

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -3.354101966 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.354101966 + -0.5
x = -3.354101966 + -0.5

Combine like terms: -3.354101966 + -0.5 = -3.854101966
x = -3.854101966

Simplifying
x = -3.854101966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.854101966, -3.854101966}

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