x^2+12x=22

Simple and best practice solution for x^2+12x=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+12x=22 equation:


Simplifying
x2 + 12x = 22

Reorder the terms:
12x + x2 = 22

Solving
12x + x2 = 22

Solving for variable 'x'.

Reorder the terms:
-22 + 12x + x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + 12x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + 12x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 12x + x2 = 0 + 22
12x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
12x + x2 = 22

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 22 + 36

Reorder the terms:
36 + 12x + x2 = 22 + 36

Combine like terms: 22 + 36 = 58
36 + 12x + x2 = 58

Factor a perfect square on the left side:
(x + 6)(x + 6) = 58

Calculate the square root of the right side: 7.615773106

Break this problem into two subproblems by setting 
(x + 6) equal to 7.615773106 and -7.615773106.

Subproblem 1

x + 6 = 7.615773106 Simplifying x + 6 = 7.615773106 Reorder the terms: 6 + x = 7.615773106 Solving 6 + x = 7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 7.615773106 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.615773106 + -6 x = 7.615773106 + -6 Combine like terms: 7.615773106 + -6 = 1.615773106 x = 1.615773106 Simplifying x = 1.615773106

Subproblem 2

x + 6 = -7.615773106 Simplifying x + 6 = -7.615773106 Reorder the terms: 6 + x = -7.615773106 Solving 6 + x = -7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -7.615773106 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.615773106 + -6 x = -7.615773106 + -6 Combine like terms: -7.615773106 + -6 = -13.615773106 x = -13.615773106 Simplifying x = -13.615773106

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.615773106, -13.615773106}

See similar equations:

| 7x+6=8x+4 | | 5=4x+45 | | 8x-8=7x-6 | | 3x-2=5x-14 | | 3x^2y^2-3= | | 8d+3=3d+18 | | 9x-1=2x+6 | | (x+4)*(2x+4)=112 | | y^2-3y=2 | | x^2-8x-3= | | x+4*2x+4=112 | | 100=1.3x | | 54-4x=14x+24 | | -5(14y+18)= | | 101-3x=6x+6 | | 6(4-2d)=60 | | 3x+4y=18 | | 1-3y=-14 | | 2x+2=4x-1 | | 9x+17=6x+83 | | 7-9x=89-23x | | -3x-7=-12 | | x^2-33x+200=0 | | 12x+14=24-x | | 167-3x=24x+17 | | 10n-3=67 | | 0.1x-x= | | 7r+8s-2(6r-9s)= | | N-4.05=6.2 | | 7x-(2x+6)= | | X-23.3=17.8 | | 7x-2x^2=0 |

Equations solver categories