x^2+x=22

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


Simplifying
x2 + x = 22

Reorder the terms:
x + x2 = 22

Solving
x + x2 = 22

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 + 0.25

Reorder the terms:
0.25 + x + x2 = 22 + 0.25

Combine like terms: 22 + 0.25 = 22.25
0.25 + x + x2 = 22.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.716990566 and -4.716990566.

Subproblem 1

x + 0.5 = 4.716990566 Simplifying x + 0.5 = 4.716990566 Reorder the terms: 0.5 + x = 4.716990566 Solving 0.5 + x = 4.716990566 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 = 4.716990566 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.716990566 + -0.5 x = 4.716990566 + -0.5 Combine like terms: 4.716990566 + -0.5 = 4.216990566 x = 4.216990566 Simplifying x = 4.216990566

Subproblem 2

x + 0.5 = -4.716990566 Simplifying x + 0.5 = -4.716990566 Reorder the terms: 0.5 + x = -4.716990566 Solving 0.5 + x = -4.716990566 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 = -4.716990566 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.716990566 + -0.5 x = -4.716990566 + -0.5 Combine like terms: -4.716990566 + -0.5 = -5.216990566 x = -5.216990566 Simplifying x = -5.216990566

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.216990566, -5.216990566}

See similar equations:

| V=8(3.14)a | | 8x=50-2x | | 90=7y+4 | | 1x^4-13x^2+36=0 | | 2/a^3b^2,7/a^5b | | 4x=-x+25 | | 3(y-x)=9 | | 3(x+2)=15-(x^2+4x+4) | | x^2+6x+5=2x+2 | | x^2+8x+17=2 | | 4x+(-x)=-x+25+x | | 2+2x-34=45 | | -7y-7=3y | | (5x)=3 | | 4x+8=-x+33 | | 4-(2x-(-x+1))=3x-10 | | 2(2x-4)+2-10= | | -2-4x=2(x-1) | | -1/(-6/5)=x | | -7.5+3+(-6.5)=x | | V=1/3(18)(13) | | g-5/10=g+4/4 | | 3(x+iy)=8-12i-(x-iy) | | 3(x+iy)=8-12i-(x-iy) | | -33/28=-b/2 | | 5x+6x=300 | | 3-(-x-1)=30 | | -20-36= | | 2w-3/4-w-2/3=2 | | 17a+18b+6c+4c-4b-5a= | | 22+-1= | | 9x^2+21x=0 |

Equations solver categories