6x^2+28x-2=0

Simple and best practice solution for 6x^2+28x-2=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 6x^2+28x-2=0 equation: 


Simplifying
6x2 + 28x + -2 = 0

Reorder the terms:
-2 + 28x + 6x2 = 0

Solving
-2 + 28x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 14x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + 14x + 3x2)' equal to zero and attempt to solve:

Simplifying
-1 + 14x + 3x2 = 0

Solving
-1 + 14x + 3x2 = 0

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

Divide each side by '3'.
-0.3333333333 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 4.666666667x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 4.666666667x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 4.666666667x + x2 = 0 + 0.3333333333
4.666666667x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
4.666666667x + x2 = 0.3333333333

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 = 0.3333333333 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 0.3333333333 + 5.444444448

Combine like terms: 0.3333333333 + 5.444444448 = 5.7777777813
5.444444448 + 4.666666667x + x2 = 5.7777777813

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 5.7777777813

Calculate the square root of the right side: 2.403700851

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 2.403700851 and -2.403700851.


Subproblem 1
x + 2.333333334 = 2.403700851

Simplifying
x + 2.333333334 = 2.403700851

Reorder the terms:
2.333333334 + x = 2.403700851

Solving
2.333333334 + x = 2.403700851

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 = 2.403700851 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 2.403700851 + -2.333333334
x = 2.403700851 + -2.333333334

Combine like terms: 2.403700851 + -2.333333334 = 0.070367517
x = 0.070367517

Simplifying
x = 0.070367517


Subproblem 2
x + 2.333333334 = -2.403700851

Simplifying
x + 2.333333334 = -2.403700851

Reorder the terms:
2.333333334 + x = -2.403700851

Solving
2.333333334 + x = -2.403700851

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 = -2.403700851 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -2.403700851 + -2.333333334
x = -2.403700851 + -2.333333334

Combine like terms: -2.403700851 + -2.333333334 = -4.737034185
x = -4.737034185

Simplifying
x = -4.737034185


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.070367517, -4.737034185}
Solution
x = {0.070367517, -4.737034185}

See similar equations:

| 2(2x+4)=2x+9 | | 17-2=-3 | | 3(2x+6)=4x+3 | | 3(-3)-1/2y=2 | | 3z^2+3=6z | | 3z^2+3=6 | | x^2=725 | | 3(0)-1/2y=2 | | 3(-1)+2y=2 | | 3(-2)-1/2y=2 | | Y-5=0(x+2) | | 6(7x+5)=3x+7 | | 3(7)+Y=51 | | 1.06-3x=.71 | | 3(2x+4)=2(x+4) | | 3(2)-2y= | | 3(1)-2y=7 | | 3(0)-2y=7 | | (6x+1)+(5x+8)= | | 3(-1)+2y=7 | | 3(-2)+2y=7 | | 3(1)+2y=10 | | 2(6x+4)=3x+10 | | f(-6)=2x+8 | | 10-6a=-4a+-12 | | 3(-1)+2y=10 | | 4y-6=7y-48 | | 3(-2)+2y= | | 4(3x-1)7-x=-2x+3+9x | | 2(2x+4)=5x+4 | | (8x-3y)+(-8x+3y)=16-16 | | 3z+30=51 |

Equations solver categories