2x^2+11=x+21

Solution for 2x^2+11=x+21 equation:

Simplifying
2x2 + 11 = x + 21

Reorder the terms:
11 + 2x2 = x + 21

Reorder the terms:
11 + 2x2 = 21 + x

Solving
11 + 2x2 = 21 + x

Solving for variable 'x'.

Reorder the terms:
11 + -21 + -1x + 2x2 = 21 + x + -21 + -1x

Combine like terms: 11 + -21 = -10
-10 + -1x + 2x2 = 21 + x + -21 + -1x

Reorder the terms:
-10 + -1x + 2x2 = 21 + -21 + x + -1x

Combine like terms: 21 + -21 = 0
-10 + -1x + 2x2 = 0 + x + -1x
-10 + -1x + 2x2 = x + -1x

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

Factor a trinomial.
(-2 + -1x)(5 + -2x) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

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