8a^2+9a-6=0

Simple and best practice solution for 8a^2+9a-6=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 8a^2+9a-6=0 equation:


Simplifying
8a2 + 9a + -6 = 0

Reorder the terms:
-6 + 9a + 8a2 = 0

Solving
-6 + 9a + 8a2 = 0

Solving for variable 'a'.

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

Divide each side by '8'.
-0.75 + 1.125a + a2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 1.125a + 0.75 + a2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 1.125a + a2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 1.125a + a2 = 0 + 0.75
1.125a + a2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
1.125a + a2 = 0.75

The a term is 1.125a.  Take half its coefficient (0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
1.125a + 0.31640625 + a2 = 0.75 + 0.31640625

Reorder the terms:
0.31640625 + 1.125a + a2 = 0.75 + 0.31640625

Combine like terms: 0.75 + 0.31640625 = 1.06640625
0.31640625 + 1.125a + a2 = 1.06640625

Factor a perfect square on the left side:
(a + 0.5625)(a + 0.5625) = 1.06640625

Calculate the square root of the right side: 1.032669478

Break this problem into two subproblems by setting 
(a + 0.5625) equal to 1.032669478 and -1.032669478.

Subproblem 1

a + 0.5625 = 1.032669478 Simplifying a + 0.5625 = 1.032669478 Reorder the terms: 0.5625 + a = 1.032669478 Solving 0.5625 + a = 1.032669478 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + a = 1.032669478 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + a = 1.032669478 + -0.5625 a = 1.032669478 + -0.5625 Combine like terms: 1.032669478 + -0.5625 = 0.470169478 a = 0.470169478 Simplifying a = 0.470169478

Subproblem 2

a + 0.5625 = -1.032669478 Simplifying a + 0.5625 = -1.032669478 Reorder the terms: 0.5625 + a = -1.032669478 Solving 0.5625 + a = -1.032669478 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + a = -1.032669478 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + a = -1.032669478 + -0.5625 a = -1.032669478 + -0.5625 Combine like terms: -1.032669478 + -0.5625 = -1.595169478 a = -1.595169478 Simplifying a = -1.595169478

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.470169478, -1.595169478}

See similar equations:

| 2250+12500=a | | 12500*0.045*4=i | | -2(-5n+6)=37+3n | | f(8a)=x-9 | | 2/3r-16=14 | | 3k+12=4(k+5) | | -12+6x=-192 | | 33+4y-5=16y-12-4y | | -12+6x=192 | | 1000*0.0375*3=i | | 6(-1+r)-3r=-5r+18 | | 5x-4=3x+20+2(x-1) | | 12+6x=192 | | 1000*0.03*4=i | | -6+4=-12 | | -8(3v+1)=-40-8v | | (3x+20)+(5x-4)=180 | | -0.5m+6.4=4.9-0.1m | | -3(4+7n)-7=4n+32 | | -8-9=9x+2-8x | | 3x+x+2x-5=180 | | a=3.14v^2t | | 4-2/3x1 | | -12+7=m-2 | | 5x^5/9 | | 52=10x-13 | | y=3.6x+6.5 | | -37+5a=2(a-8) | | 9x+7-5x=6+3x+2 | | 200=0.008x^2+.518x+131.886 | | 3V+8=-4 | | 5r-30=-3(2-3r) |

Equations solver categories