6x^2-55x+84=0

Simple and best practice solution for 6x^2-55x+84=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^2-55x+84=0 equation: 


Simplifying
6x2 + -55x + 84 = 0

Reorder the terms:
84 + -55x + 6x2 = 0

Solving
84 + -55x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
14 + -9.166666667x + x2 = 0

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -9.166666667x + -14 + x2 = 0 + -14

Reorder the terms:
14 + -14 + -9.166666667x + x2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -9.166666667x + x2 = 0 + -14
-9.166666667x + x2 = 0 + -14

Combine like terms: 0 + -14 = -14
-9.166666667x + x2 = -14

The x term is -9.166666667x.  Take half its coefficient (-4.583333334).
Square it (21.00694445) and add it to both sides.

Add '21.00694445' to each side of the equation.
-9.166666667x + 21.00694445 + x2 = -14 + 21.00694445

Reorder the terms:
21.00694445 + -9.166666667x + x2 = -14 + 21.00694445

Combine like terms: -14 + 21.00694445 = 7.00694445
21.00694445 + -9.166666667x + x2 = 7.00694445

Factor a perfect square on the left side:
(x + -4.583333334)(x + -4.583333334) = 7.00694445

Calculate the square root of the right side: 2.647063363

Break this problem into two subproblems by setting 
(x + -4.583333334) equal to 2.647063363 and -2.647063363.


Subproblem 1
x + -4.583333334 = 2.647063363

Simplifying
x + -4.583333334 = 2.647063363

Reorder the terms:
-4.583333334 + x = 2.647063363

Solving
-4.583333334 + x = 2.647063363

Solving for variable 'x'.

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

Add '4.583333334' to each side of the equation.
-4.583333334 + 4.583333334 + x = 2.647063363 + 4.583333334

Combine like terms: -4.583333334 + 4.583333334 = 0.000000000
0.000000000 + x = 2.647063363 + 4.583333334
x = 2.647063363 + 4.583333334

Combine like terms: 2.647063363 + 4.583333334 = 7.230396697
x = 7.230396697

Simplifying
x = 7.230396697


Subproblem 2
x + -4.583333334 = -2.647063363

Simplifying
x + -4.583333334 = -2.647063363

Reorder the terms:
-4.583333334 + x = -2.647063363

Solving
-4.583333334 + x = -2.647063363

Solving for variable 'x'.

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

Add '4.583333334' to each side of the equation.
-4.583333334 + 4.583333334 + x = -2.647063363 + 4.583333334

Combine like terms: -4.583333334 + 4.583333334 = 0.000000000
0.000000000 + x = -2.647063363 + 4.583333334
x = -2.647063363 + 4.583333334

Combine like terms: -2.647063363 + 4.583333334 = 1.936269971
x = 1.936269971

Simplifying
x = 1.936269971


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.230396697, 1.936269971}

See similar equations:

| 2(5x+3)-2x=62 | | 2(u-2)-7=-3(-5u+3)-3u | | -2(-4-7x)=92 | | 9(3a+2)=-63 | | 8+125=173x | | 25-1-36= | | x^4+18x^2-37x+81=0 | | 245+x=290 | | (138.9)-(-78.8)= | | 4x^5-64x^3=0 | | 1+30=31 | | 2z^2+21z+10=0 | | 2x+4(3x-1)=38 | | 28x+20=188 | | -78.8-(138.9)= | | -16.5-81.5= | | 93-x=87 | | (-78.8)-138.9= | | 0.10x+.45(70)=36.5 | | 4x+4-2(-5x-3)=2(x-2) | | 7(1+1x)=77 | | 7(1+1x)=76 | | -78.8-138.9= | | M+15=6m | | .875+.25= | | 2.3n=9.2 | | 6m-15= | | 3t=8/3t | | 5n+3=14-6nm | | 010+045(70)=36.5 | | 93-x=86 | | 3t=12/9(2t) |

Equations solver categories