a^2+21a-2=0

Simple and best practice solution for a^2+21a-2=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+21a-2=0 equation:


Simplifying
a2 + 21a + -2 = 0

Reorder the terms:
-2 + 21a + a2 = 0

Solving
-2 + 21a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 21a + 2 + a2 = 0 + 2

Reorder the terms:
-2 + 2 + 21a + a2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 21a + a2 = 0 + 2
21a + a2 = 0 + 2

Combine like terms: 0 + 2 = 2
21a + a2 = 2

The a term is 21a.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21a + 110.25 + a2 = 2 + 110.25

Reorder the terms:
110.25 + 21a + a2 = 2 + 110.25

Combine like terms: 2 + 110.25 = 112.25
110.25 + 21a + a2 = 112.25

Factor a perfect square on the left side:
(a + 10.5)(a + 10.5) = 112.25

Calculate the square root of the right side: 10.59481005

Break this problem into two subproblems by setting 
(a + 10.5) equal to 10.59481005 and -10.59481005.


Subproblem 1
a + 10.5 = 10.59481005

Simplifying
a + 10.5 = 10.59481005

Reorder the terms:
10.5 + a = 10.59481005

Solving
10.5 + a = 10.59481005

Solving for variable 'a'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + a = 10.59481005 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + a = 10.59481005 + -10.5
a = 10.59481005 + -10.5

Combine like terms: 10.59481005 + -10.5 = 0.09481005
a = 0.09481005

Simplifying
a = 0.09481005


Subproblem 2
a + 10.5 = -10.59481005

Simplifying
a + 10.5 = -10.59481005

Reorder the terms:
10.5 + a = -10.59481005

Solving
10.5 + a = -10.59481005

Solving for variable 'a'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + a = -10.59481005 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + a = -10.59481005 + -10.5
a = -10.59481005 + -10.5

Combine like terms: -10.59481005 + -10.5 = -21.09481005
a = -21.09481005

Simplifying
a = -21.09481005


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.09481005, -21.09481005}

See similar equations:

| 12+v/7=7 | | 9=x*24 | | 9=x*25 | | 18r+1=109 | | 7y-12=20 | | n+1/11=-2 | | 4(2-(-2))=4 | | 7y-22=30 | | 7n^2+11n-6=0 | | x-2/8-1=x-2/4 | | v/2-5=-9 | | -6-4a=-74 | | 5/3+2/3x=25/2+5/4x+3/4 | | 7(6x-1)+x=3 | | -2+k/3=1 | | 10x^3+5x=6x^3+3 | | 11+3r=-34 | | 5+5n=-50 | | 7(x-5)=-168 | | 75*3=5x | | x/5-3=-1 | | -9(v+9)=-171 | | -1+x/7=3 | | 3/4x+16=52 | | 10y=5y-15 | | 8m-3=-59 | | 12*15=60x | | -8+n-3=-5 | | 0=-4.9x^2+19.6x+58.8 | | -10(-2+x)=-110 | | 11+/2=4 | | a+6/18=-1 |

Equations solver categories