3x^2-32x+60=0

Simple and best practice solution for 3x^2-32x+60=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^2-32x+60=0 equation: 


Simplifying
3x2 + -32x + 60 = 0

Reorder the terms:
60 + -32x + 3x2 = 0

Solving
60 + -32x + 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'.
20 + -10.66666667x + x2 = 0

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -10.66666667x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -10.66666667x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -10.66666667x + x2 = 0 + -20
-10.66666667x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-10.66666667x + x2 = -20

The x term is -10.66666667x.  Take half its coefficient (-5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
-10.66666667x + 28.44444446 + x2 = -20 + 28.44444446

Reorder the terms:
28.44444446 + -10.66666667x + x2 = -20 + 28.44444446

Combine like terms: -20 + 28.44444446 = 8.44444446
28.44444446 + -10.66666667x + x2 = 8.44444446

Factor a perfect square on the left side:
(x + -5.333333335)(x + -5.333333335) = 8.44444446

Calculate the square root of the right side: 2.905932632

Break this problem into two subproblems by setting 
(x + -5.333333335) equal to 2.905932632 and -2.905932632.


Subproblem 1
x + -5.333333335 = 2.905932632

Simplifying
x + -5.333333335 = 2.905932632

Reorder the terms:
-5.333333335 + x = 2.905932632

Solving
-5.333333335 + x = 2.905932632

Solving for variable 'x'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + x = 2.905932632 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + x = 2.905932632 + 5.333333335
x = 2.905932632 + 5.333333335

Combine like terms: 2.905932632 + 5.333333335 = 8.239265967
x = 8.239265967

Simplifying
x = 8.239265967


Subproblem 2
x + -5.333333335 = -2.905932632

Simplifying
x + -5.333333335 = -2.905932632

Reorder the terms:
-5.333333335 + x = -2.905932632

Solving
-5.333333335 + x = -2.905932632

Solving for variable 'x'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + x = -2.905932632 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + x = -2.905932632 + 5.333333335
x = -2.905932632 + 5.333333335

Combine like terms: -2.905932632 + 5.333333335 = 2.427400703
x = 2.427400703

Simplifying
x = 2.427400703


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.239265967, 2.427400703}

See similar equations:

| 5(7x+6)=275 | | 9x=5x+100 | | 25x^3+5x^2=0 | | 5(5+x)=30 | | -4(5)-8(5)= | | -5+25(5)-40(5)-10= | | 5(2x+2)=110 | | 4tanx+9=0 | | m-8=3 | | 2c+(3c-4)=25 | | 14=5g-6 | | 7n-6+n=(4n-3) | | 5(6+7x)=275 | | 5x+4x-8=-2x-3 | | 5s=5+15+5 | | 27+3x=21 | | 8a-3=5 | | -85y^9/-5 | | 5-10x+3x=11 | | 2b+6=7b+-2 | | (5u-6)(4+u)=0 | | 100=.885x | | x+.31*x=17049 | | 5/6-1/2y-5/7 | | (-2/11)*(-11/2) | | 3b+9=10b-3 | | -10(3-x)=30 | | 39-4x=11-8x | | 2x+x-7=290 | | 4(2x+1)=5x+3(x-2) | | 2x+5=-15-2x | | -10(3-x)=11 |

Equations solver categories