3x^2+32x+21=0

Simple and best practice solution for 3x^2+32x+21=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+21=0 equation: 


Simplifying
3x2 + 32x + 21 = 0

Reorder the terms:
21 + 32x + 3x2 = 0

Solving
21 + 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'.
7 + 10.66666667x + x2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 10.66666667x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 10.66666667x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 10.66666667x + x2 = 0 + -7
10.66666667x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
10.66666667x + x2 = -7

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 = -7 + 28.44444446

Reorder the terms:
28.44444446 + 10.66666667x + x2 = -7 + 28.44444446

Combine like terms: -7 + 28.44444446 = 21.44444446
28.44444446 + 10.66666667x + x2 = 21.44444446

Factor a perfect square on the left side:
(x + 5.333333335)(x + 5.333333335) = 21.44444446

Calculate the square root of the right side: 4.630814665

Break this problem into two subproblems by setting 
(x + 5.333333335) equal to 4.630814665 and -4.630814665.


Subproblem 1
x + 5.333333335 = 4.630814665

Simplifying
x + 5.333333335 = 4.630814665

Reorder the terms:
5.333333335 + x = 4.630814665

Solving
5.333333335 + x = 4.630814665

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 = 4.630814665 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + x = 4.630814665 + -5.333333335
x = 4.630814665 + -5.333333335

Combine like terms: 4.630814665 + -5.333333335 = -0.70251867
x = -0.70251867

Simplifying
x = -0.70251867


Subproblem 2
x + 5.333333335 = -4.630814665

Simplifying
x + 5.333333335 = -4.630814665

Reorder the terms:
5.333333335 + x = -4.630814665

Solving
5.333333335 + x = -4.630814665

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 = -4.630814665 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + x = -4.630814665 + -5.333333335
x = -4.630814665 + -5.333333335

Combine like terms: -4.630814665 + -5.333333335 = -9.964148
x = -9.964148

Simplifying
x = -9.964148


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.70251867, -9.964148}

See similar equations:

| 7x*110=90 | | (.66)3x+2= | | 11x-69=29+4x | | 265=-x+85 | | 14x+14x=x+18 | | 7X*110=180 | | x^5-x^4-2x^3+2x^2-24x+24=0 | | 7+3n+3n+n=63 | | 9x-208=-6x+62 | | 101-v=277 | | D+8-5+2D=27 | | (2+16)+58=90 | | 7x-2=10x+4-9 | | -141+2x=12x+79 | | 48x^3-24x^2+3x=0 | | 2x-8+2x-8=3x-6 | | 9t-3t-7=11 | | -54-11x=x+126 | | 43=6x+3x+7 | | 15+3k+8+2k=73 | | 5x-1=2x-1 | | 5(z-2)+3(z-6)= | | 2(n+1)=3n-2 | | X+18+x+18=x+25 | | 9n^2+7=-104 | | 31+4x=39 | | 25+2x-18=15 | | 84=7h | | 8x^2+4x=O | | 2(n-1)=3(n+2)-9 | | -2x+5-4x=-7 | | X*2=3x-7 |

Equations solver categories