3x^2-16x-21=0

Simple and best practice solution for 3x^2-16x-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^2-16x-21=0 equation: 


Simplifying
3x2 + -16x + -21 = 0

Reorder the terms:
-21 + -16x + 3x2 = 0

Solving
-21 + -16x + 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 + -5.333333333x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -5.333333333x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -5.333333333x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5.333333333x + x2 = 0 + 7
-5.333333333x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-5.333333333x + x2 = 7

The x term is -5.333333333x.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333x + 7.111111113 + x2 = 7 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333x + x2 = 7 + 7.111111113

Combine like terms: 7 + 7.111111113 = 14.111111113
7.111111113 + -5.333333333x + x2 = 14.111111113

Factor a perfect square on the left side:
(x + -2.666666667)(x + -2.666666667) = 14.111111113

Calculate the square root of the right side: 3.75647589

Break this problem into two subproblems by setting 
(x + -2.666666667) equal to 3.75647589 and -3.75647589.


Subproblem 1
x + -2.666666667 = 3.75647589

Simplifying
x + -2.666666667 = 3.75647589

Reorder the terms:
-2.666666667 + x = 3.75647589

Solving
-2.666666667 + x = 3.75647589

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = 3.75647589 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = 3.75647589 + 2.666666667
x = 3.75647589 + 2.666666667

Combine like terms: 3.75647589 + 2.666666667 = 6.423142557
x = 6.423142557

Simplifying
x = 6.423142557


Subproblem 2
x + -2.666666667 = -3.75647589

Simplifying
x + -2.666666667 = -3.75647589

Reorder the terms:
-2.666666667 + x = -3.75647589

Solving
-2.666666667 + x = -3.75647589

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = -3.75647589 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = -3.75647589 + 2.666666667
x = -3.75647589 + 2.666666667

Combine like terms: -3.75647589 + 2.666666667 = -1.089809223
x = -1.089809223

Simplifying
x = -1.089809223


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.423142557, -1.089809223}

See similar equations:

| 4(3x+2)-7=3x-2 | | (2x-5)(x-4)+2x(1-x)=0 | | 5(t-2)+3= | | -3.5r+3r=1.3r+31.3 | | 3/5-5/16= | | 18=2*x-12 | | -x-7=11(x-11)-6(2x-6) | | y=2*1-12 | | 3(t-4)+3= | | 5x+34=75x | | 4x+6=2x-5+x | | 8x+15=3x+15 | | 23-19=2(x-6) | | 1=2x(x-2)-(5-2x(1-x)) | | 2g-5/8=g+5/8 | | x+6=(-3x+3) | | 5r-2r+4=6r-r | | 3(x+2)=5x+6-2x | | 2(x+3)-3=3x-4-x | | 8x+4=7+4x | | (4-x)3=36 | | 4(t-4)+10= | | 5x-16=-81 | | 12(11x+7)-5(1+9x)=-95 | | 25+5y-2=16y-13-2y | | f(20)=100 | | 4s^2+12s-9=0 | | 0.3x=x-140 | | -5-(15-1)=2(7x-16)-x | | -2x^2+6x-10=0 | | X+18+4x=-42-4x-48 | | 6t^2=-18t |

Equations solver categories