3q^2-19q-76=0

Simple and best practice solution for 3q^2-19q-76=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 3q^2-19q-76=0 equation: 


Simplifying
3q2 + -19q + -76 = 0

Reorder the terms:
-76 + -19q + 3q2 = 0

Solving
-76 + -19q + 3q2 = 0

Solving for variable 'q'.

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

Divide each side by '3'.
-25.33333333 + -6.333333333q + q2 = 0

Move the constant term to the right:

Add '25.33333333' to each side of the equation.
-25.33333333 + -6.333333333q + 25.33333333 + q2 = 0 + 25.33333333

Reorder the terms:
-25.33333333 + 25.33333333 + -6.333333333q + q2 = 0 + 25.33333333

Combine like terms: -25.33333333 + 25.33333333 = 0.00000000
0.00000000 + -6.333333333q + q2 = 0 + 25.33333333
-6.333333333q + q2 = 0 + 25.33333333

Combine like terms: 0 + 25.33333333 = 25.33333333
-6.333333333q + q2 = 25.33333333

The q term is -6.333333333q.  Take half its coefficient (-3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
-6.333333333q + 10.02777778 + q2 = 25.33333333 + 10.02777778

Reorder the terms:
10.02777778 + -6.333333333q + q2 = 25.33333333 + 10.02777778

Combine like terms: 25.33333333 + 10.02777778 = 35.36111111
10.02777778 + -6.333333333q + q2 = 35.36111111

Factor a perfect square on the left side:
(q + -3.166666667)(q + -3.166666667) = 35.36111111

Calculate the square root of the right side: 5.946520925

Break this problem into two subproblems by setting 
(q + -3.166666667) equal to 5.946520925 and -5.946520925.


Subproblem 1
q + -3.166666667 = 5.946520925

Simplifying
q + -3.166666667 = 5.946520925

Reorder the terms:
-3.166666667 + q = 5.946520925

Solving
-3.166666667 + q = 5.946520925

Solving for variable 'q'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + q = 5.946520925 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + q = 5.946520925 + 3.166666667
q = 5.946520925 + 3.166666667

Combine like terms: 5.946520925 + 3.166666667 = 9.113187592
q = 9.113187592

Simplifying
q = 9.113187592


Subproblem 2
q + -3.166666667 = -5.946520925

Simplifying
q + -3.166666667 = -5.946520925

Reorder the terms:
-3.166666667 + q = -5.946520925

Solving
-3.166666667 + q = -5.946520925

Solving for variable 'q'.

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

Add '3.166666667' to each side of the equation.
-3.166666667 + 3.166666667 + q = -5.946520925 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + q = -5.946520925 + 3.166666667
q = -5.946520925 + 3.166666667

Combine like terms: -5.946520925 + 3.166666667 = -2.779854258
q = -2.779854258

Simplifying
q = -2.779854258


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {9.113187592, -2.779854258}

See similar equations:

| y-4x=80 | | 4x-4y=150 | | .50x=12-5 | | 16x+4x+8x=180 | | 4/sqrt(x)=2 | | -7x-8-3x=42 | | x-2x+x=7 | | 4x-4y=30 | | m-14=m+14 | | -9/5=x | | 9x^2-2=73 | | 9x^2+-2=73 | | 9x-10y=75 | | a=2x+3y | | 30=-5n(6p+6) | | -5x+4-4x=76 | | -1.25x=-8+2 | | -1.25x=8+2 | | 1/5x=605 | | 1.25x=-2-8 | | 4x+2(-3x+6)=8 | | 4x-2+3x-7=51 | | 1.25x=8-2 | | y^2-12y-36=0 | | -1.25x=2+8 | | 8x+1=27x+4 | | 4x^2-x+5=x+9 | | -1.25x=8-2 | | 6(2n+2)=6(6n+3)+2 | | (4x^2)-x+5=x+9 | | -1.25x=8-6 | | -3/8y=3/16-9/16 |

Equations solver categories