37x^2-252x+189=0

Simple and best practice solution for 37x^2-252x+189=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 37x^2-252x+189=0 equation: 


Simplifying
37x2 + -252x + 189 = 0

Reorder the terms:
189 + -252x + 37x2 = 0

Solving
189 + -252x + 37x2 = 0

Solving for variable 'x'.

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

Divide each side by '37'.
5.108108108 + -6.810810811x + x2 = 0

Move the constant term to the right:

Add '-5.108108108' to each side of the equation.
5.108108108 + -6.810810811x + -5.108108108 + x2 = 0 + -5.108108108

Reorder the terms:
5.108108108 + -5.108108108 + -6.810810811x + x2 = 0 + -5.108108108

Combine like terms: 5.108108108 + -5.108108108 = 0.000000000
0.000000000 + -6.810810811x + x2 = 0 + -5.108108108
-6.810810811x + x2 = 0 + -5.108108108

Combine like terms: 0 + -5.108108108 = -5.108108108
-6.810810811x + x2 = -5.108108108

The x term is -6.810810811x.  Take half its coefficient (-3.405405406).
Square it (11.59678598) and add it to both sides.

Add '11.59678598' to each side of the equation.
-6.810810811x + 11.59678598 + x2 = -5.108108108 + 11.59678598

Reorder the terms:
11.59678598 + -6.810810811x + x2 = -5.108108108 + 11.59678598

Combine like terms: -5.108108108 + 11.59678598 = 6.488677872
11.59678598 + -6.810810811x + x2 = 6.488677872

Factor a perfect square on the left side:
(x + -3.405405406)(x + -3.405405406) = 6.488677872

Calculate the square root of the right side: 2.547288337

Break this problem into two subproblems by setting 
(x + -3.405405406) equal to 2.547288337 and -2.547288337.


Subproblem 1
x + -3.405405406 = 2.547288337

Simplifying
x + -3.405405406 = 2.547288337

Reorder the terms:
-3.405405406 + x = 2.547288337

Solving
-3.405405406 + x = 2.547288337

Solving for variable 'x'.

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

Add '3.405405406' to each side of the equation.
-3.405405406 + 3.405405406 + x = 2.547288337 + 3.405405406

Combine like terms: -3.405405406 + 3.405405406 = 0.000000000
0.000000000 + x = 2.547288337 + 3.405405406
x = 2.547288337 + 3.405405406

Combine like terms: 2.547288337 + 3.405405406 = 5.952693743
x = 5.952693743

Simplifying
x = 5.952693743


Subproblem 2
x + -3.405405406 = -2.547288337

Simplifying
x + -3.405405406 = -2.547288337

Reorder the terms:
-3.405405406 + x = -2.547288337

Solving
-3.405405406 + x = -2.547288337

Solving for variable 'x'.

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

Add '3.405405406' to each side of the equation.
-3.405405406 + 3.405405406 + x = -2.547288337 + 3.405405406

Combine like terms: -3.405405406 + 3.405405406 = 0.000000000
0.000000000 + x = -2.547288337 + 3.405405406
x = -2.547288337 + 3.405405406

Combine like terms: -2.547288337 + 3.405405406 = 0.858117069
x = 0.858117069

Simplifying
x = 0.858117069


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.952693743, 0.858117069}

See similar equations:

| 2.1-0.2x=0 | | y+4-x=y+8-2x | | 2x/7=1/3 | | (-x+4)-(-7x+6)= | | (-x+4)-(7x+6)= | | x/3-9x=9 | | 5c-2+6=-6 | | 0=-16x^2-22x+344 | | 4(4a+3)-9= | | b-2b=40+4b | | 4x-6=24x | | 4x+28-2x=x+20 | | -9-5x+6=-16x+7-5x | | 15=3ln(4x) | | 8*n=20 | | n*3=17 | | y+4=y+8 | | (4a/5b)(15b/16a) | | -5y+6y+5=-8+1 | | y=2E-05x^1 | | 3-6=y-7 | | X-11/3=-7 | | 16x^2-6x+1= | | 3*y=24 | | 3timesy=24 | | F(x)=8(0.8)x | | .125x=9 | | 48=4t^2 | | -4f^2+4=0 | | d^2-4d-5=0 | | (9g^10)^-1/2 | | -9w^2+6w-1=0 |

Equations solver categories