3x^2-14x+4=0

Simple and best practice solution for 3x^2-14x+4=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 3x^2-14x+4=0 equation: 


Simplifying
3x2 + -14x + 4 = 0

Reorder the terms:
4 + -14x + 3x2 = 0

Solving
4 + -14x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
1.333333333 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -4.666666667x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -4.666666667x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -4.666666667x + x2 = 0 + -1.333333333
-4.666666667x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-4.666666667x + x2 = -1.333333333

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = -1.333333333 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = -1.333333333 + 5.444444448

Combine like terms: -1.333333333 + 5.444444448 = 4.111111115
5.444444448 + -4.666666667x + x2 = 4.111111115

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 4.111111115

Calculate the square root of the right side: 2.027587511

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 2.027587511 and -2.027587511.


Subproblem 1
x + -2.333333334 = 2.027587511

Simplifying
x + -2.333333334 = 2.027587511

Reorder the terms:
-2.333333334 + x = 2.027587511

Solving
-2.333333334 + x = 2.027587511

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 2.027587511 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 2.027587511 + 2.333333334
x = 2.027587511 + 2.333333334

Combine like terms: 2.027587511 + 2.333333334 = 4.360920845
x = 4.360920845

Simplifying
x = 4.360920845


Subproblem 2
x + -2.333333334 = -2.027587511

Simplifying
x + -2.333333334 = -2.027587511

Reorder the terms:
-2.333333334 + x = -2.027587511

Solving
-2.333333334 + x = -2.027587511

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -2.027587511 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -2.027587511 + 2.333333334
x = -2.027587511 + 2.333333334

Combine like terms: -2.027587511 + 2.333333334 = 0.305745823
x = 0.305745823

Simplifying
x = 0.305745823


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.360920845, 0.305745823}

See similar equations:

| 12(1/6)= | | 22/3+3n=4/5n+15 | | 3x+3=2x+26 | | 0.60x-0.20(40+x)=0.30(40) | | 1/3f=2/3f+4 | | 4(x+4)-2/-5=3x+8 | | n^2+n=4200 | | 0.18(y-1)+0.08=0.10y-1.5 | | 44p+7=73 | | 24=4x-9-x | | 13/18x=21 | | 7q+8=-27 | | 3.6/n=22/15 | | 4x+3=45 | | 1/12n+5=27 | | 3(6a-2)-(5a-5)= | | 12v+14+10v=8 | | 3p-8/5=11 | | .30x+2=11 | | 35d+1(-7+7d)+1= | | 11+4/3b=35 | | 1/9*2x | | 3/4y+1/4=7/4 | | -5(-3-c)+4=5c-11 | | 3/10d=45 | | 2k-6k+3k=14 | | 7x^3+4x^2-252x-144=0 | | 3x-1.3=x+6.5 | | 4/7p-3=29 | | -k/9+6=-14 | | -17-2c=6-c | | .25x+8=2 |

Equations solver categories