x^2+22x-204=0

Simple and best practice solution for x^2+22x-204=0 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+22x-204=0 equation: 


Simplifying
x2 + 22x + -204 = 0

Reorder the terms:
-204 + 22x + x2 = 0

Solving
-204 + 22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '204' to each side of the equation.
-204 + 22x + 204 + x2 = 0 + 204

Reorder the terms:
-204 + 204 + 22x + x2 = 0 + 204

Combine like terms: -204 + 204 = 0
0 + 22x + x2 = 0 + 204
22x + x2 = 0 + 204

Combine like terms: 0 + 204 = 204
22x + x2 = 204

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = 204 + 121

Reorder the terms:
121 + 22x + x2 = 204 + 121

Combine like terms: 204 + 121 = 325
121 + 22x + x2 = 325

Factor a perfect square on the left side:
(x + 11)(x + 11) = 325

Calculate the square root of the right side: 18.027756377

Break this problem into two subproblems by setting 
(x + 11) equal to 18.027756377 and -18.027756377.


Subproblem 1
x + 11 = 18.027756377

Simplifying
x + 11 = 18.027756377

Reorder the terms:
11 + x = 18.027756377

Solving
11 + x = 18.027756377

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = 18.027756377 + -11

Combine like terms: 11 + -11 = 0
0 + x = 18.027756377 + -11
x = 18.027756377 + -11

Combine like terms: 18.027756377 + -11 = 7.027756377
x = 7.027756377

Simplifying
x = 7.027756377


Subproblem 2
x + 11 = -18.027756377

Simplifying
x + 11 = -18.027756377

Reorder the terms:
11 + x = -18.027756377

Solving
11 + x = -18.027756377

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = -18.027756377 + -11

Combine like terms: 11 + -11 = 0
0 + x = -18.027756377 + -11
x = -18.027756377 + -11

Combine like terms: -18.027756377 + -11 = -29.027756377
x = -29.027756377

Simplifying
x = -29.027756377


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.027756377, -29.027756377}

See similar equations:

| (x)(x)+10x-21=0 | | (8x-3)=(5x+4) | | 49x^2+16y^2=9 | | (x-.25x)-(.40x)= | | 4x^2-19x+12x=0 | | 3e^2(x)-1=28 | | (1000-.25)-(.40)= | | -3+4-5*2= | | 3x+4x=6x-4 | | 2x+cosx=0 | | 2m+7-3(m+4)= | | 10-2a=1a+1 | | 1.2x+4.3=2.1+x | | 10x+-4x+12=6x+4 | | 3-(2+3x)= | | 5+4(5n-3)-5n= | | [5z+6]=[z+2] | | 3=2c+10 | | 43-5x=19+7x | | 239*45= | | -3a+4=2a-6 | | 30x^2+50x=0 | | 43+2(53-2)-2= | | 2e^2x=4e^5x | | 8d+(4d+2)= | | (33ab+22bc-11b^2)=0 | | 2-2(3+4)= | | 5x^2+4x=204 | | 2x+3+x+8=11 | | 9Q(3Q-1)(3Q+1)= | | (5-n)-2=5+(n-2) | | 2(6d+3)=-30+9d |

Equations solver categories