a^2-13a+18=0

Simple and best practice solution for a^2-13a+18=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^2-13a+18=0 equation: 


Simplifying
a2 + -13a + 18 = 0

Reorder the terms:
18 + -13a + a2 = 0

Solving
18 + -13a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -13a + -18 + a2 = 0 + -18

Reorder the terms:
18 + -18 + -13a + a2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -13a + a2 = 0 + -18
-13a + a2 = 0 + -18

Combine like terms: 0 + -18 = -18
-13a + a2 = -18

The a term is -13a.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13a + 42.25 + a2 = -18 + 42.25

Reorder the terms:
42.25 + -13a + a2 = -18 + 42.25

Combine like terms: -18 + 42.25 = 24.25
42.25 + -13a + a2 = 24.25

Factor a perfect square on the left side:
(a + -6.5)(a + -6.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(a + -6.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
a + -6.5 = 4.924428901

Simplifying
a + -6.5 = 4.924428901

Reorder the terms:
-6.5 + a = 4.924428901

Solving
-6.5 + a = 4.924428901

Solving for variable 'a'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + a = 4.924428901 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + a = 4.924428901 + 6.5
a = 4.924428901 + 6.5

Combine like terms: 4.924428901 + 6.5 = 11.424428901
a = 11.424428901

Simplifying
a = 11.424428901


Subproblem 2
a + -6.5 = -4.924428901

Simplifying
a + -6.5 = -4.924428901

Reorder the terms:
-6.5 + a = -4.924428901

Solving
-6.5 + a = -4.924428901

Solving for variable 'a'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + a = -4.924428901 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + a = -4.924428901 + 6.5
a = -4.924428901 + 6.5

Combine like terms: -4.924428901 + 6.5 = 1.575571099
a = 1.575571099

Simplifying
a = 1.575571099


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {11.424428901, 1.575571099}

See similar equations:

| z+0.6=1.3 | | 6(x-2)+3(4-2x)=2x+1 | | r+-4=-2 | | 105+(45+2x)=180 | | v-5.0=6.3 | | 24-6x=15x | | 5.99=m+c | | 2x(x)=900 | | -6x+(-5+3)=-7x+4x-7 | | 46+y=91 | | 90=14x+34 | | 6x+(-5+3)=-7x+4x-7 | | w+1=71 | | y=20x^3+-3x^5 | | 56*3-76/4= | | m-17=-9 | | a^2-10a-2000=0 | | 80-2x=96-3x | | m-39=67 | | 4x+8=-2+5x | | n(n+1)=156 | | 26+x=93 | | 44-3*4= | | a^2-10a-2100=0 | | 1/2x-6.512 | | n+-14=5 | | (x-5)^(5/3)-73=170 | | 60*n=9 | | 37+m=307 | | 36p^2+4=0 | | 207-8x=27 | | 55+n=81 |

Equations solver categories