3x^2-10x-21=0

Simple and best practice solution for 3x^2-10x-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^2-10x-21=0 equation: 


Simplifying
3x2 + -10x + -21 = 0

Reorder the terms:
-21 + -10x + 3x2 = 0

Solving
-21 + -10x + 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 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -3.333333333x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -3.333333333x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3.333333333x + x2 = 0 + 7
-3.333333333x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-3.333333333x + x2 = 7

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 7 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 7 + 2.777777779

Combine like terms: 7 + 2.777777779 = 9.777777779
2.777777779 + -3.333333333x + x2 = 9.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 9.777777779

Calculate the square root of the right side: 3.12694384

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 3.12694384 and -3.12694384.


Subproblem 1
x + -1.666666667 = 3.12694384

Simplifying
x + -1.666666667 = 3.12694384

Reorder the terms:
-1.666666667 + x = 3.12694384

Solving
-1.666666667 + x = 3.12694384

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 3.12694384 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 3.12694384 + 1.666666667
x = 3.12694384 + 1.666666667

Combine like terms: 3.12694384 + 1.666666667 = 4.793610507
x = 4.793610507

Simplifying
x = 4.793610507


Subproblem 2
x + -1.666666667 = -3.12694384

Simplifying
x + -1.666666667 = -3.12694384

Reorder the terms:
-1.666666667 + x = -3.12694384

Solving
-1.666666667 + x = -3.12694384

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -3.12694384 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -3.12694384 + 1.666666667
x = -3.12694384 + 1.666666667

Combine like terms: -3.12694384 + 1.666666667 = -1.460277173
x = -1.460277173

Simplifying
x = -1.460277173


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.793610507, -1.460277173}

See similar equations:

| -10=-4+x | | -6(0.461538462)+4y=8 | | 33y=8(4y-7) | | 3x+5y-3x+2y= | | -6-7=7x+10-6x | | 9y+20= | | 4y=5u | | -18+3x=-x+30 | | ax+2y=-2 | | 8-14=z/-9 | | 2x+1x-5=36 | | 3y+17=-2+25 | | ax+by=10 | | -3(x+5)-10=4(x+5)+3x | | m=71-65 | | 10w-18w=24 | | a=(-2)+5x(-3) | | -8(-5b+7)5b= | | -3(x-5)-10=4(x+5)+3x | | 24/x=5-1.5 | | 6y+10=7+1 | | x+9+6=52 | | -4x-19=-83 | | -30+10x=5x+40 | | 108+69+(5x+27)+(4x+3)=360 | | 9v^2-5=-8v | | -3(n-10)=27 | | X*1/5=60 | | -5x+9x-13+2x-16=-71 | | z+1=18 | | a=-2+5x-3 | | 3y+4=21 |

Equations solver categories