x^2+x=22.5

Simple and best practice solution for x^2+x=22.5 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for x^2+x=22.5 equation: 


Simplifying
x2 + x = 22.5

Reorder the terms:
x + x2 = 22.5

Solving
x + x2 = 22.5

Solving for variable 'x'.

Reorder the terms:
-22.5 + x + x2 = 22.5 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
-22.5 + x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '22.5' to each side of the equation.
-22.5 + x + 22.5 + x2 = 0.0 + 22.5

Reorder the terms:
-22.5 + 22.5 + x + x2 = 0.0 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + x + x2 = 0.0 + 22.5
x + x2 = 0.0 + 22.5

Combine like terms: 0.0 + 22.5 = 22.5
x + x2 = 22.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 22.5 + 0.25

Reorder the terms:
0.25 + x + x2 = 22.5 + 0.25

Combine like terms: 22.5 + 0.25 = 22.75
0.25 + x + x2 = 22.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 22.75

Calculate the square root of the right side: 4.769696007

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.769696007 and -4.769696007.


Subproblem 1
x + 0.5 = 4.769696007

Simplifying
x + 0.5 = 4.769696007

Reorder the terms:
0.5 + x = 4.769696007

Solving
0.5 + x = 4.769696007

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 4.769696007 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4.769696007 + -0.5
x = 4.769696007 + -0.5

Combine like terms: 4.769696007 + -0.5 = 4.269696007
x = 4.269696007

Simplifying
x = 4.269696007


Subproblem 2
x + 0.5 = -4.769696007

Simplifying
x + 0.5 = -4.769696007

Reorder the terms:
0.5 + x = -4.769696007

Solving
0.5 + x = -4.769696007

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -4.769696007 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4.769696007 + -0.5
x = -4.769696007 + -0.5

Combine like terms: -4.769696007 + -0.5 = -5.269696007
x = -5.269696007

Simplifying
x = -5.269696007


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.269696007, -5.269696007}

See similar equations:

| 0.4+0.3=0.8x-0.9 | | 9x^2-78x-26=0 | | P(X)=4x+2 | | 4n+2.3=7.9 | | x+y-z-t=0 | | 4x+21+2x+73=360 | | (5v-3)(6+v)=0 | | 2x^2+2x+1=41 | | 5(x-2)+3(x+1)=25 | | 5ax+b+bx+5a= | | 4000/x=60/100 | | -32a=4 | | 60/100=4000 | | 32=y-10 | | 7x-29/(x-2)(x-2)(x=30 | | M-15=80 | | 2xsquared+4=54 | | 15/5=y:40 | | 13-b/6=2-9.5b/4 | | 5(2-3x)-17(-2x-5)=16 | | 4.62=-6.6y | | 30=3r | | 12=-5+v | | 25=-5c | | (-5p^8q^15)^3/-5p^6q^40)^2 | | (3x-5y)-(8x+18y)= | | 10=-6+b | | (x^2)-x=1 | | 5n/6=100 | | 2/3=b=1/4 | | 4/x-x/2=7/2 | | 3(x-1)=22 |

Equations solver categories