x^2+9x+15+x=11

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Solution for x^2+9x+15+x=11 equation:


Simplifying
x2 + 9x + 15 + x = 11

Reorder the terms:
15 + 9x + x + x2 = 11

Combine like terms: 9x + x = 10x
15 + 10x + x2 = 11

Solving
15 + 10x + x2 = 11

Solving for variable 'x'.

Reorder the terms:
15 + -11 + 10x + x2 = 11 + -11

Combine like terms: 15 + -11 = 4
4 + 10x + x2 = 11 + -11

Combine like terms: 11 + -11 = 0
4 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 10x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 10x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 10x + x2 = 0 + -4
10x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
10x + x2 = -4

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -4 + 25

Reorder the terms:
25 + 10x + x2 = -4 + 25

Combine like terms: -4 + 25 = 21
25 + 10x + x2 = 21

Factor a perfect square on the left side:
(x + 5)(x + 5) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + 5) equal to 4.582575695 and -4.582575695.

Subproblem 1

x + 5 = 4.582575695 Simplifying x + 5 = 4.582575695 Reorder the terms: 5 + x = 4.582575695 Solving 5 + x = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.582575695 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.582575695 + -5 x = 4.582575695 + -5 Combine like terms: 4.582575695 + -5 = -0.417424305 x = -0.417424305 Simplifying x = -0.417424305

Subproblem 2

x + 5 = -4.582575695 Simplifying x + 5 = -4.582575695 Reorder the terms: 5 + x = -4.582575695 Solving 5 + x = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.582575695 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.582575695 + -5 x = -4.582575695 + -5 Combine like terms: -4.582575695 + -5 = -9.582575695 x = -9.582575695 Simplifying x = -9.582575695

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.417424305, -9.582575695}

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