12a^2-11a-8=0

Simple and best practice solution for 12a^2-11a-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 12a^2-11a-8=0 equation: 


Simplifying
12a2 + -11a + -8 = 0

Reorder the terms:
-8 + -11a + 12a2 = 0

Solving
-8 + -11a + 12a2 = 0

Solving for variable 'a'.

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

Divide each side by '12'.
-0.6666666667 + -0.9166666667a + a2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -0.9166666667a + 0.6666666667 + a2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -0.9166666667a + a2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -0.9166666667a + a2 = 0 + 0.6666666667
-0.9166666667a + a2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-0.9166666667a + a2 = 0.6666666667

The a term is -0.9166666667a.  Take half its coefficient (-0.4583333334).
Square it (0.2100694445) and add it to both sides.

Add '0.2100694445' to each side of the equation.
-0.9166666667a + 0.2100694445 + a2 = 0.6666666667 + 0.2100694445

Reorder the terms:
0.2100694445 + -0.9166666667a + a2 = 0.6666666667 + 0.2100694445

Combine like terms: 0.6666666667 + 0.2100694445 = 0.8767361112
0.2100694445 + -0.9166666667a + a2 = 0.8767361112

Factor a perfect square on the left side:
(a + -0.4583333334)(a + -0.4583333334) = 0.8767361112

Calculate the square root of the right side: 0.936341877

Break this problem into two subproblems by setting 
(a + -0.4583333334) equal to 0.936341877 and -0.936341877.


Subproblem 1
a + -0.4583333334 = 0.936341877

Simplifying
a + -0.4583333334 = 0.936341877

Reorder the terms:
-0.4583333334 + a = 0.936341877

Solving
-0.4583333334 + a = 0.936341877

Solving for variable 'a'.

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

Add '0.4583333334' to each side of the equation.
-0.4583333334 + 0.4583333334 + a = 0.936341877 + 0.4583333334

Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000
0.0000000000 + a = 0.936341877 + 0.4583333334
a = 0.936341877 + 0.4583333334

Combine like terms: 0.936341877 + 0.4583333334 = 1.3946752104
a = 1.3946752104

Simplifying
a = 1.3946752104


Subproblem 2
a + -0.4583333334 = -0.936341877

Simplifying
a + -0.4583333334 = -0.936341877

Reorder the terms:
-0.4583333334 + a = -0.936341877

Solving
-0.4583333334 + a = -0.936341877

Solving for variable 'a'.

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

Add '0.4583333334' to each side of the equation.
-0.4583333334 + 0.4583333334 + a = -0.936341877 + 0.4583333334

Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000
0.0000000000 + a = -0.936341877 + 0.4583333334
a = -0.936341877 + 0.4583333334

Combine like terms: -0.936341877 + 0.4583333334 = -0.4780085436
a = -0.4780085436

Simplifying
a = -0.4780085436


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.3946752104, -0.4780085436}

See similar equations:

| -4y-7=y | | 2x^2-3x+8=0 | | 3t+15=2t+2 | | 2(x^2+14x+85)=0 | | (10+x)(3x-11)= | | ln(2x)+6=4 | | x^2+14x+85=0 | | -2(x-4)=-2 | | 7x+5+3x=15 | | -2x+7=10 | | 28X^2-29X-9=0 | | x^2+7x=30 | | 77=x+7x+5+8 | | x*4+y*2=106 | | 6v^2+19v-7=0 | | -3x^2-x-3=0 | | (13x^2+7x-15)+(8x^2-15x-9)= | | (x+3)(x-6)=0 | | (3x-4)(2x-2)= | | (7c+4)(3c-9)=0 | | 5x^2(7x^3)= | | 1.7x-1.8y+4.8x-0.7y= | | 8x=x^2-9 | | 2.4+[(-1.6)+(-1.3)]= | | 3a^2-12a+12=0 | | 24=2L+2(4) | | 560=8t | | 8r+12s-4r= | | x+7*2.5=20 | | -0.08(50)+0.80x=0.40(50+x) | | 4(y+5)=5(y-8) | | 8a^4+7a^2b-b^2=0 |

Equations solver categories