4a^2-31a+8=0

Simple and best practice solution for 4a^2-31a+8=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 4a^2-31a+8=0 equation: 


Simplifying
4a2 + -31a + 8 = 0

Reorder the terms:
8 + -31a + 4a2 = 0

Solving
8 + -31a + 4a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
2 + -7.75a + a2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -7.75a + -2 + a2 = 0 + -2

Reorder the terms:
2 + -2 + -7.75a + a2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7.75a + a2 = 0 + -2
-7.75a + a2 = 0 + -2

Combine like terms: 0 + -2 = -2
-7.75a + a2 = -2

The a term is -7.75a.  Take half its coefficient (-3.875).
Square it (15.015625) and add it to both sides.

Add '15.015625' to each side of the equation.
-7.75a + 15.015625 + a2 = -2 + 15.015625

Reorder the terms:
15.015625 + -7.75a + a2 = -2 + 15.015625

Combine like terms: -2 + 15.015625 = 13.015625
15.015625 + -7.75a + a2 = 13.015625

Factor a perfect square on the left side:
(a + -3.875)(a + -3.875) = 13.015625

Calculate the square root of the right side: 3.607717422

Break this problem into two subproblems by setting 
(a + -3.875) equal to 3.607717422 and -3.607717422.


Subproblem 1
a + -3.875 = 3.607717422

Simplifying
a + -3.875 = 3.607717422

Reorder the terms:
-3.875 + a = 3.607717422

Solving
-3.875 + a = 3.607717422

Solving for variable 'a'.

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

Add '3.875' to each side of the equation.
-3.875 + 3.875 + a = 3.607717422 + 3.875

Combine like terms: -3.875 + 3.875 = 0.000
0.000 + a = 3.607717422 + 3.875
a = 3.607717422 + 3.875

Combine like terms: 3.607717422 + 3.875 = 7.482717422
a = 7.482717422

Simplifying
a = 7.482717422


Subproblem 2
a + -3.875 = -3.607717422

Simplifying
a + -3.875 = -3.607717422

Reorder the terms:
-3.875 + a = -3.607717422

Solving
-3.875 + a = -3.607717422

Solving for variable 'a'.

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

Add '3.875' to each side of the equation.
-3.875 + 3.875 + a = -3.607717422 + 3.875

Combine like terms: -3.875 + 3.875 = 0.000
0.000 + a = -3.607717422 + 3.875
a = -3.607717422 + 3.875

Combine like terms: -3.607717422 + 3.875 = 0.267282578
a = 0.267282578

Simplifying
a = 0.267282578


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {7.482717422, 0.267282578}

See similar equations:

| 8x+9y=Txy | | 90x-3=300(4x-3) | | 4s(s-4)=0 | | 9s(s-4)=0 | | 4x(x-9)(x+9)=0 | | 6p-p=x | | 6p-p=5p | | 6p-6=5p | | y=200-10x | | b^2-10b+k=0 | | b^2-10b= | | (y+4)8= | | 2x^6-4x^3+2=0 | | 4(y-9)=-10 | | b^2-10b+k=25 | | 6(2w-9)=-66 | | b^2-10b+k=3 | | 2(x^6-2x^3+1)=0 | | 0.15*15=x | | 30a−5/5a−1 | | 2x+3y=763 | | -2w=50 | | (-n+6)(-3n-23)=0 | | √64x/2x^2 | | c*x*y+(c^2)x+4=0 | | 2/9,2/3,8/21 | | x=9x+23 | | 3n^2+5n-138=0 | | 3/10,7/18 | | (P-2)(3p-9)=0 | | 5x^3-80=0 | | 16x^2=144 |

Equations solver categories