21x^2+105x+28=0

Simple and best practice solution for 21x^2+105x+28=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 21x^2+105x+28=0 equation:


Simplifying
21x2 + 105x + 28 = 0

Reorder the terms:
28 + 105x + 21x2 = 0

Solving
28 + 105x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(4 + 15x + 3x2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(4 + 15x + 3x2)' equal to zero and attempt to solve:

Simplifying
4 + 15x + 3x2 = 0

Solving
4 + 15x + 3x2 = 0

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

Divide each side by '3'.
1.333333333 + 5x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 5x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 5x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 5x + x2 = 0 + -1.333333333
5x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
5x + x2 = -1.333333333

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -1.333333333 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -1.333333333 + 6.25

Combine like terms: -1.333333333 + 6.25 = 4.916666667
6.25 + 5x + x2 = 4.916666667

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 4.916666667

Calculate the square root of the right side: 2.217355783

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.217355783 and -2.217355783.


Subproblem 1
x + 2.5 = 2.217355783

Simplifying
x + 2.5 = 2.217355783

Reorder the terms:
2.5 + x = 2.217355783

Solving
2.5 + x = 2.217355783

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.217355783 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.217355783 + -2.5
x = 2.217355783 + -2.5

Combine like terms: 2.217355783 + -2.5 = -0.282644217
x = -0.282644217

Simplifying
x = -0.282644217


Subproblem 2
x + 2.5 = -2.217355783

Simplifying
x + 2.5 = -2.217355783

Reorder the terms:
2.5 + x = -2.217355783

Solving
2.5 + x = -2.217355783

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.217355783 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.217355783 + -2.5
x = -2.217355783 + -2.5

Combine like terms: -2.217355783 + -2.5 = -4.717355783
x = -4.717355783

Simplifying
x = -4.717355783


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.282644217, -4.717355783}
Solution
x = {-0.282644217, -4.717355783}

See similar equations:

| 5a-2=6(a+4) | | 24=m/-5+17 | | 5/6-(-3/2) | | ((y^2/4)3.14)-((x^2/4)3.14) | | -11/12+1/18 | | g/12+(-8)=-5 | | 2/21/(-2/35) | | 14.95+0.13m=50 | | 4v+5=13 | | 21/77/3/28 | | 4x-50=9x+80 | | -3/2*14/15 | | -2(2b+3)+(5b-5)=0 | | x^2+3=199 | | 6+6r-5=9r+6-2r | | -15.00+0.39m=50 | | 4.3q-2.9-5.1q=1.8q-2.2 | | 13r-(-12)=103 | | 151=x+2x+(x+11) | | 12(4x-8)=4(12+2) | | 15=d/2-(-12) | | 8s+13s=105 | | x*(624-2x/3) | | 4.3-2.9-5.1=1.8-2.2 | | 6x^2-13x+16=0 | | 5/15*10/175 | | 5+3t-2=7t+8-3t | | -11z+42=86 | | y/16=-12 | | (v+3)(v+1)=15 | | 3/21*9 | | -6*1/30 |

Equations solver categories