x+9=2*x*x-1*1

Solution for x+9=2*x*x-1*1 equation:

Simplifying
x + 9 = 2x * x + -1 * 1

Reorder the terms:
9 + x = 2x * x + -1 * 1

Multiply x * x
9 + x = 2x2 + -1 * 1

Multiply -1 * 1
9 + x = 2x2 + -1

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

Solving
9 + x = -1 + 2x2

Solving for variable 'x'.

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

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

Reorder the terms:
10 + x + -2x2 = -1 + 1 + 2x2 + -2x2

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

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

Factor a trinomial.
(5 + -2x)(2 + x) = 0

Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Solution
x = {2.5, -2}