x^2+x(x+3)=-1x+18

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Solution for x^2+x(x+3)=-1x+18 equation: 


Simplifying
x2 + x(x + 3) = -1x + 18

Reorder the terms:
x2 + x(3 + x) = -1x + 18
x2 + (3 * x + x * x) = -1x + 18
x2 + (3x + x2) = -1x + 18

Reorder the terms:
3x + x2 + x2 = -1x + 18

Combine like terms: x2 + x2 = 2x2
3x + 2x2 = -1x + 18

Reorder the terms:
3x + 2x2 = 18 + -1x

Solving
3x + 2x2 = 18 + -1x

Solving for variable 'x'.

Reorder the terms:
-18 + 3x + x + 2x2 = 18 + -1x + -18 + x

Combine like terms: 3x + x = 4x
-18 + 4x + 2x2 = 18 + -1x + -18 + x

Reorder the terms:
-18 + 4x + 2x2 = 18 + -18 + -1x + x

Combine like terms: 18 + -18 = 0
-18 + 4x + 2x2 = 0 + -1x + x
-18 + 4x + 2x2 = -1x + x

Combine like terms: -1x + x = 0
-18 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + 2x + x2 = 0

Solving
-9 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 2x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 2x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2x + x2 = 0 + 9
2x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
2x + x2 = 9

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 9 + 1

Reorder the terms:
1 + 2x + x2 = 9 + 1

Combine like terms: 9 + 1 = 10
1 + 2x + x2 = 10

Factor a perfect square on the left side:
(x + 1)(x + 1) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 1) equal to 3.16227766 and -3.16227766.


Subproblem 1
x + 1 = 3.16227766

Simplifying
x + 1 = 3.16227766

Reorder the terms:
1 + x = 3.16227766

Solving
1 + x = 3.16227766

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 3.16227766 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.16227766 + -1
x = 3.16227766 + -1

Combine like terms: 3.16227766 + -1 = 2.16227766
x = 2.16227766

Simplifying
x = 2.16227766


Subproblem 2
x + 1 = -3.16227766

Simplifying
x + 1 = -3.16227766

Reorder the terms:
1 + x = -3.16227766

Solving
1 + x = -3.16227766

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -3.16227766 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.16227766 + -1
x = -3.16227766 + -1

Combine like terms: -3.16227766 + -1 = -4.16227766
x = -4.16227766

Simplifying
x = -4.16227766


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.16227766, -4.16227766}
Solution
x = {2.16227766, -4.16227766}

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