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 = 48.44444446
28.44444446 + 10.66666667x + x2 = 48.44444446

Factor a perfect square on the left side:
(x + 5.333333335)(x + 5.333333335) = 48.44444446

Calculate the square root of the right side: 6.96020434

Break this problem into two subproblems by setting 
(x + 5.333333335) equal to 6.96020434 and -6.96020434.


Subproblem 1
x + 5.333333335 = 6.96020434

Simplifying
x + 5.333333335 = 6.96020434

Reorder the terms:
5.333333335 + x = 6.96020434

Solving
5.333333335 + x = 6.96020434

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 = 6.96020434 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + x = 6.96020434 + -5.333333335
x = 6.96020434 + -5.333333335

Combine like terms: 6.96020434 + -5.333333335 = 1.626871005
x = 1.626871005

Simplifying
x = 1.626871005


Subproblem 2
x + 5.333333335 = -6.96020434

Simplifying
x + 5.333333335 = -6.96020434

Reorder the terms:
5.333333335 + x = -6.96020434

Solving
5.333333335 + x = -6.96020434

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 = -6.96020434 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + x = -6.96020434 + -5.333333335
x = -6.96020434 + -5.333333335

Combine like terms: -6.96020434 + -5.333333335 = -12.293537675
x = -12.293537675

Simplifying
x = -12.293537675


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.626871005, -12.293537675}

See similar equations:

| 6w^2-5w-14=0 | | c-16c+63=0 | | 2x^2+12x-15=0 | | a^2+8a-1=0 | | 3.6x=2.4x*7.2 | | b^2-2b-7=0 | | 14x-7=x+23 | | x/2+4=-6 | | 10y=4y^2 | | 6x+4=5x+7 | | x^2+18x+76=0 | | 8x^2+10x-2x^3=0 | | 10y+30=10y-30 | | 44x^3-14x^2-4x=0 | | 12x^2+12x+3=0 | | 3x+9=36 | | 3x^3=-81 | | 8x^5-2x^4+4x^2-4x=GFC | | 3x^2+xy+y^2=2 | | y=0.04x^2+8.3x+4.3 | | x^4+14x^2+13=0 | | -4-13=6y+17 | | 25x^2-2x+4=-22x | | 17=t-6 | | 25x^2-9x+9=-39x | | (4x+5)(2x-5)=0 | | (x-8)(x+4)=-2(x-8) | | 2x^2+7x=9x | | 3-4t=19 | | 6x^2=45x-75 | | x+3x+5=1000 | | 6x^2=40x-50 |

Equations solver categories