3r^2-10r-3=0

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


Simplifying
3r2 + -10r + -3 = 0

Reorder the terms:
-3 + -10r + 3r2 = 0

Solving
-3 + -10r + 3r2 = 0

Solving for variable 'r'.

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

Divide each side by '3'.
-1 + -3.333333333r + r2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3.333333333r + 1 + r2 = 0 + 1

Reorder the terms:
-1 + 1 + -3.333333333r + r2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3.333333333r + r2 = 0 + 1
-3.333333333r + r2 = 0 + 1

Combine like terms: 0 + 1 = 1
-3.333333333r + r2 = 1

The r term is -3.333333333r.  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.
-3.333333333r + 2.777777779 + r2 = 1 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333r + r2 = 1 + 2.777777779

Combine like terms: 1 + 2.777777779 = 3.777777779
2.777777779 + -3.333333333r + r2 = 3.777777779

Factor a perfect square on the left side:
(r + -1.666666667)(r + -1.666666667) = 3.777777779

Calculate the square root of the right side: 1.943650632

Break this problem into two subproblems by setting 
(r + -1.666666667) equal to 1.943650632 and -1.943650632.


Subproblem 1
r + -1.666666667 = 1.943650632

Simplifying
r + -1.666666667 = 1.943650632

Reorder the terms:
-1.666666667 + r = 1.943650632

Solving
-1.666666667 + r = 1.943650632

Solving for variable 'r'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + r = 1.943650632 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + r = 1.943650632 + 1.666666667
r = 1.943650632 + 1.666666667

Combine like terms: 1.943650632 + 1.666666667 = 3.610317299
r = 3.610317299

Simplifying
r = 3.610317299


Subproblem 2
r + -1.666666667 = -1.943650632

Simplifying
r + -1.666666667 = -1.943650632

Reorder the terms:
-1.666666667 + r = -1.943650632

Solving
-1.666666667 + r = -1.943650632

Solving for variable 'r'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + r = -1.943650632 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + r = -1.943650632 + 1.666666667
r = -1.943650632 + 1.666666667

Combine like terms: -1.943650632 + 1.666666667 = -0.276983965
r = -0.276983965

Simplifying
r = -0.276983965


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.610317299, -0.276983965}

See similar equations:

| -12=32-9n | | C/4-19=17 | | 2i/4-3i | | -2(x+6)+3=-11x+4(x+14) | | 7y-2y=30 | | 3c+2+5c=4 | | 9(2)+10= | | 5+3=-35 | | -8+12x-11x=14 | | 8sinx=4cos^2x-7 | | 4(8n-1)=19+32 | | 3-7=15 | | 2(14.5)+5+6(14.5)-1=120 | | 6a-2a=-36answer | | ln(x+1)=ln(3x) | | 3-4i/1-2i | | 9x+-6x=24 | | 2x-39=6(6x+8)-5 | | 14.18+0.05=y | | F(x)=300-x | | 13x-11y=-11 | | x^2+1=13 | | -10=4x+2(-6x+15) | | 9(-1/6)=10= | | y=0.05x+14.18 | | 12y=16y^2 | | 9/1.5 | | 5=-(1+C)-(14+2C) | | -13+n= | | 1+x=1738 | | -10=4x+2(-6+15) | | 1.5/9 |

Equations solver categories