x^2+11x+10=9

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Solution for x^2+11x+10=9 equation:


Simplifying
x2 + 11x + 10 = 9

Reorder the terms:
10 + 11x + x2 = 9

Solving
10 + 11x + x2 = 9

Solving for variable 'x'.

Reorder the terms:
10 + -9 + 11x + x2 = 9 + -9

Combine like terms: 10 + -9 = 1
1 + 11x + x2 = 9 + -9

Combine like terms: 9 + -9 = 0
1 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 11x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 11x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 11x + x2 = 0 + -1
11x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
11x + x2 = -1

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 = -1 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -1 + 30.25

Combine like terms: -1 + 30.25 = 29.25
30.25 + 11x + x2 = 29.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 29.25

Calculate the square root of the right side: 5.408326913

Break this problem into two subproblems by setting 
(x + 5.5) equal to 5.408326913 and -5.408326913.

Subproblem 1

x + 5.5 = 5.408326913 Simplifying x + 5.5 = 5.408326913 Reorder the terms: 5.5 + x = 5.408326913 Solving 5.5 + x = 5.408326913 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 = 5.408326913 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 5.408326913 + -5.5 x = 5.408326913 + -5.5 Combine like terms: 5.408326913 + -5.5 = -0.091673087 x = -0.091673087 Simplifying x = -0.091673087

Subproblem 2

x + 5.5 = -5.408326913 Simplifying x + 5.5 = -5.408326913 Reorder the terms: 5.5 + x = -5.408326913 Solving 5.5 + x = -5.408326913 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 = -5.408326913 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -5.408326913 + -5.5 x = -5.408326913 + -5.5 Combine like terms: -5.408326913 + -5.5 = -10.908326913 x = -10.908326913 Simplifying x = -10.908326913

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.091673087, -10.908326913}

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