3x^2-21x-5=0

Simple and best practice solution for 3x^2-21x-5=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^2-21x-5=0 equation:


Simplifying
3x2 + -21x + -5 = 0

Reorder the terms:
-5 + -21x + 3x2 = 0

Solving
-5 + -21x + 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'.
-1.666666667 + -7x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -7x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -7x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -7x + x2 = 0 + 1.666666667
-7x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-7x + x2 = 1.666666667

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 1.666666667 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 1.666666667 + 12.25

Combine like terms: 1.666666667 + 12.25 = 13.916666667
12.25 + -7x + x2 = 13.916666667

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 13.916666667

Calculate the square root of the right side: 3.730504881

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.730504881 and -3.730504881.

Subproblem 1

x + -3.5 = 3.730504881 Simplifying x + -3.5 = 3.730504881 Reorder the terms: -3.5 + x = 3.730504881 Solving -3.5 + x = 3.730504881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.730504881 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.730504881 + 3.5 x = 3.730504881 + 3.5 Combine like terms: 3.730504881 + 3.5 = 7.230504881 x = 7.230504881 Simplifying x = 7.230504881

Subproblem 2

x + -3.5 = -3.730504881 Simplifying x + -3.5 = -3.730504881 Reorder the terms: -3.5 + x = -3.730504881 Solving -3.5 + x = -3.730504881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.730504881 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.730504881 + 3.5 x = -3.730504881 + 3.5 Combine like terms: -3.730504881 + 3.5 = -0.230504881 x = -0.230504881 Simplifying x = -0.230504881

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.230504881, -0.230504881}

See similar equations:

| x/7=33/35 | | 6/19=2x/874 | | 7x+14y=9 | | 8a-24=3a+1 | | W^2+2w-6=0 | | 7n+8=20 | | 14m=6n | | 3-(m-2)=-2m-3(m+7) | | 7x-6=-6+20 | | 3(4x+3)=2x-5(3-c)+2 | | 2x-5+6x+4= | | 7x+35x=5x-8 | | 0.2y-0.25=0.50 | | 12n-30=-21+11n | | x-4+4+(x-2)(x+1)=0 | | a^2+10ab-39b=0 | | x-8=15x+4 | | 5/4=x-3/3 | | 8a=15+3a | | 11(3m)-11(m)= | | x^2-6xy+5y=0 | | 4(x+1)=8(2x+3) | | 8x-8y=-112 | | 13x=5x+8 | | (5+2)=(4-x) | | 4n-1.2=0.24 | | 200-5x=30 | | -0.31x=-1.705 | | 3y-17=43 | | 4(2-3x)=5(2-3x) | | 2.5x=-8.3 | | x+4y+3z=8 |

Equations solver categories