12x^2-12x-374=0

Simple and best practice solution for 12x^2-12x-374=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 12x^2-12x-374=0 equation: 


Simplifying
12x2 + -12x + -374 = 0

Reorder the terms:
-374 + -12x + 12x2 = 0

Solving
-374 + -12x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-187 + -6x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-187 + -6x + 6x2)' equal to zero and attempt to solve:

Simplifying
-187 + -6x + 6x2 = 0

Solving
-187 + -6x + 6x2 = 0

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

Divide each side by '6'.
-31.16666667 + -1x + x2 = 0

Move the constant term to the right:

Add '31.16666667' to each side of the equation.
-31.16666667 + -1x + 31.16666667 + x2 = 0 + 31.16666667

Reorder the terms:
-31.16666667 + 31.16666667 + -1x + x2 = 0 + 31.16666667

Combine like terms: -31.16666667 + 31.16666667 = 0.00000000
0.00000000 + -1x + x2 = 0 + 31.16666667
-1x + x2 = 0 + 31.16666667

Combine like terms: 0 + 31.16666667 = 31.16666667
-1x + x2 = 31.16666667

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 31.16666667 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 31.16666667 + 0.25

Combine like terms: 31.16666667 + 0.25 = 31.41666667
0.25 + -1x + x2 = 31.41666667

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 31.41666667

Calculate the square root of the right side: 5.605057241

Break this problem into two subproblems by setting 
(x + -0.5) equal to 5.605057241 and -5.605057241.


Subproblem 1
x + -0.5 = 5.605057241

Simplifying
x + -0.5 = 5.605057241

Reorder the terms:
-0.5 + x = 5.605057241

Solving
-0.5 + x = 5.605057241

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 5.605057241 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 5.605057241 + 0.5
x = 5.605057241 + 0.5

Combine like terms: 5.605057241 + 0.5 = 6.105057241
x = 6.105057241

Simplifying
x = 6.105057241


Subproblem 2
x + -0.5 = -5.605057241

Simplifying
x + -0.5 = -5.605057241

Reorder the terms:
-0.5 + x = -5.605057241

Solving
-0.5 + x = -5.605057241

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -5.605057241 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -5.605057241 + 0.5
x = -5.605057241 + 0.5

Combine like terms: -5.605057241 + 0.5 = -5.105057241
x = -5.105057241

Simplifying
x = -5.105057241


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.105057241, -5.105057241}
Solution
x = {6.105057241, -5.105057241}

See similar equations:

| ln(0.132)-lnx=30.8 | | x+.03x=2000 | | (x^2)+5x+2=0 | | 136-6m=58 | | x^2+y+1600=0 | | x^2+y^2+1600=0 | | 25a-31=294 | | 25a-31=24 | | 3a-2b=45 | | 7x-6(x)+90=180 | | y=6-10x | | 2x^2+6y^2-6=0 | | 5(3k+4m)-4(3k-2m)= | | 8y+71=207 | | 4xy=0 | | 3(5p+2)-2(5p-3)= | | (5x^2)-10x=4x+3 | | x^5-x^3-20=0 | | (5z-3)-(-2z+9)= | | 26=-9u-2u-18 | | (y^2)+3y+2=0 | | 6y+37+3y=7 | | 3y-7=10-4y | | x*2x=800 | | 40-5x=12-9x | | 81U^6-4y^4=0 | | 4x^2-41x+46=0 | | 2x^2+xy-3y^2=3 | | 8x+25=6x+61 | | 3a+a=36 | | (x-3)+(x+5)+2x=32 | | 7x+6x+12x=175 |

Equations solver categories