a^2-22a+113=0

Simple and best practice solution for a^2-22a+113=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 a^2-22a+113=0 equation: 


Simplifying
a2 + -22a + 113 = 0

Reorder the terms:
113 + -22a + a2 = 0

Solving
113 + -22a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-113' to each side of the equation.
113 + -22a + -113 + a2 = 0 + -113

Reorder the terms:
113 + -113 + -22a + a2 = 0 + -113

Combine like terms: 113 + -113 = 0
0 + -22a + a2 = 0 + -113
-22a + a2 = 0 + -113

Combine like terms: 0 + -113 = -113
-22a + a2 = -113

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

Add '121' to each side of the equation.
-22a + 121 + a2 = -113 + 121

Reorder the terms:
121 + -22a + a2 = -113 + 121

Combine like terms: -113 + 121 = 8
121 + -22a + a2 = 8

Factor a perfect square on the left side:
(a + -11)(a + -11) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(a + -11) equal to 2.828427125 and -2.828427125.


Subproblem 1
a + -11 = 2.828427125

Simplifying
a + -11 = 2.828427125

Reorder the terms:
-11 + a = 2.828427125

Solving
-11 + a = 2.828427125

Solving for variable 'a'.

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

Add '11' to each side of the equation.
-11 + 11 + a = 2.828427125 + 11

Combine like terms: -11 + 11 = 0
0 + a = 2.828427125 + 11
a = 2.828427125 + 11

Combine like terms: 2.828427125 + 11 = 13.828427125
a = 13.828427125

Simplifying
a = 13.828427125


Subproblem 2
a + -11 = -2.828427125

Simplifying
a + -11 = -2.828427125

Reorder the terms:
-11 + a = -2.828427125

Solving
-11 + a = -2.828427125

Solving for variable 'a'.

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

Add '11' to each side of the equation.
-11 + 11 + a = -2.828427125 + 11

Combine like terms: -11 + 11 = 0
0 + a = -2.828427125 + 11
a = -2.828427125 + 11

Combine like terms: -2.828427125 + 11 = 8.171572875
a = 8.171572875

Simplifying
a = 8.171572875


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {13.828427125, 8.171572875}

See similar equations:

| 2.50/r=21.50 | | y+(180.5+10)=180 | | -59-4x=46+x | | 5(x+2)=2(x+15) | | 4-9+7-x+4-9=0 | | -8x-46=x+35 | | -3r+9=-4+5 | | 2a-6=2a-14 | | 22=4x-8 | | 4x+1+x=41 | | 6+4-y=-6+8+10 | | =2lnx | | y+(z+10)=180 | | -3x-6=-4x+14 | | ln(x+2)-ln(4x+3)=-lnx | | 5x+8=-7x+-13 | | 3-8(-7x+5)=-6x-37 | | 2k+7=3 | | -47-7x=9x+97 | | 6(c)=18 | | 8p+4(4x-3)=4(6x+4)-4 | | -x+2-5=4-7+1 | | 3x^2-2x-165=0 | | 5=15-24a | | 4.5=0.15p | | 9x-115=-6x+50 | | 112=2m | | 56v^2+121v+63=0 | | .66x=8 | | 180.5+w=180 | | -31-5x=59+x | | 3(q-2)+2=5q-6-2q |

Equations solver categories