3x^2+15x-21=0

Simple and best practice solution for 3x^2+15x-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+15x-21=0 equation: 


Simplifying
3x2 + 15x + -21 = 0

Reorder the terms:
-21 + 15x + 3x2 = 0

Solving
-21 + 15x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 5x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-7 + 5x + x2 = 0

Solving
-7 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 5x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 5x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 5x + x2 = 0 + 7
5x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
5x + x2 = 7

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 = 7 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 7 + 6.25

Combine like terms: 7 + 6.25 = 13.25
6.25 + 5x + x2 = 13.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.640054945 and -3.640054945.


Subproblem 1
x + 2.5 = 3.640054945

Simplifying
x + 2.5 = 3.640054945

Reorder the terms:
2.5 + x = 3.640054945

Solving
2.5 + x = 3.640054945

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 = 3.640054945 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.640054945 + -2.5
x = 3.640054945 + -2.5

Combine like terms: 3.640054945 + -2.5 = 1.140054945
x = 1.140054945

Simplifying
x = 1.140054945


Subproblem 2
x + 2.5 = -3.640054945

Simplifying
x + 2.5 = -3.640054945

Reorder the terms:
2.5 + x = -3.640054945

Solving
2.5 + x = -3.640054945

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 = -3.640054945 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.640054945 + -2.5
x = -3.640054945 + -2.5

Combine like terms: -3.640054945 + -2.5 = -6.140054945
x = -6.140054945

Simplifying
x = -6.140054945


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.140054945, -6.140054945}
Solution
x = {1.140054945, -6.140054945}

See similar equations:

| 5(x-11)=3x-41 | | x^2+2x-10=5 | | 0.15x+25=71.50 | | -5(7y+3)= | | -8x^2=-512 | | 2y-9=5y+19 | | 6-4x=12+2x | | 10x-3x+0.25x-4.25x+5=-4 | | 10x-3x+0.25x-4.25+5x=-4 | | (3*3)v+10=9v+9 | | -7(X+3)-16=14+5 | | (4-4+5)w=25 | | X(3x-23)=8 | | 35-11=3(X-1) | | 9Y-1=4Y+9 | | 4-2(2)= | | 2[15+3(x-1)]=4(x+7) | | 6r+r^2=27 | | 3.14*27= | | 15y=15y-4 | | 15y=15y-60 | | 5*6-5(4)= | | (2x^2-4x+4)(-2x^2-5x+4)= | | 2w-7(w-2)=(W-4) | | 7(1+C)=6(C-2) | | 18=4x+3 | | 3x^4+2x+5=0 | | -17=2x-8 | | 3-2(-2)= | | 2y+8=45 | | 100=0.05t | | 65x=800 |

Equations solver categories