5a^2+8a-31=0

Simple and best practice solution for 5a^2+8a-31=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 5a^2+8a-31=0 equation:


Simplifying
5a2 + 8a + -31 = 0

Reorder the terms:
-31 + 8a + 5a2 = 0

Solving
-31 + 8a + 5a2 = 0

Solving for variable 'a'.

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

Divide each side by '5'.
-6.2 + 1.6a + a2 = 0

Move the constant term to the right:

Add '6.2' to each side of the equation.
-6.2 + 1.6a + 6.2 + a2 = 0 + 6.2

Reorder the terms:
-6.2 + 6.2 + 1.6a + a2 = 0 + 6.2

Combine like terms: -6.2 + 6.2 = 0.0
0.0 + 1.6a + a2 = 0 + 6.2
1.6a + a2 = 0 + 6.2

Combine like terms: 0 + 6.2 = 6.2
1.6a + a2 = 6.2

The a term is 1.6a.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6a + 0.64 + a2 = 6.2 + 0.64

Reorder the terms:
0.64 + 1.6a + a2 = 6.2 + 0.64

Combine like terms: 6.2 + 0.64 = 6.84
0.64 + 1.6a + a2 = 6.84

Factor a perfect square on the left side:
(a + 0.8)(a + 0.8) = 6.84

Calculate the square root of the right side: 2.615339366

Break this problem into two subproblems by setting 
(a + 0.8) equal to 2.615339366 and -2.615339366.

Subproblem 1

a + 0.8 = 2.615339366 Simplifying a + 0.8 = 2.615339366 Reorder the terms: 0.8 + a = 2.615339366 Solving 0.8 + a = 2.615339366 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + a = 2.615339366 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + a = 2.615339366 + -0.8 a = 2.615339366 + -0.8 Combine like terms: 2.615339366 + -0.8 = 1.815339366 a = 1.815339366 Simplifying a = 1.815339366

Subproblem 2

a + 0.8 = -2.615339366 Simplifying a + 0.8 = -2.615339366 Reorder the terms: 0.8 + a = -2.615339366 Solving 0.8 + a = -2.615339366 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + a = -2.615339366 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + a = -2.615339366 + -0.8 a = -2.615339366 + -0.8 Combine like terms: -2.615339366 + -0.8 = -3.415339366 a = -3.415339366 Simplifying a = -3.415339366

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.815339366, -3.415339366}

See similar equations:

| W-3= | | X^7-2x^4-3=0 | | 5m^2+2m-3=0 | | 4[8-6(8x-9)]=192x+248 | | 0.4(c+8.5)=18 | | -4+4(m-7)=3(6-7m) | | 11j+-5j=18 | | 61=18+j+6+17 | | -c+-4c=5 | | (4x+7)(x-1)=2(x-21) | | 2X^2-13X-20=0 | | 8.4(x-4.25)=-33.6 | | 11-(4x-24)=7 | | 6j-13=-16.4 | | 3(b+15)=-3 | | 17-4x=45-6x | | 10(3y+4)+40= | | 0.4t=0.4+0.2t | | 3x^2+4=4 | | 2n+1+1+6n=6(n-5)+8(1+n) | | (3x^6y)(-2x^5y^3)= | | (4x+8)(2x+5)= | | 16-2x=-4 | | (6X-7)(X+1)= | | 10(3y+4)+(-40)= | | 11x-3=-18 | | -6(7x-7)+1=-42x+43 | | 27y-12y^3= | | 87-K=19 | | F(x)=2(x+10) | | c=5b-200 | | 1x-1y=9 |

Equations solver categories