-3r^2-16r-7=5

Simple and best practice solution for -3r^2-16r-7=5 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^2-16r-7=5 equation: 


Simplifying
-3r2 + -16r + -7 = 5

Reorder the terms:
-7 + -16r + -3r2 = 5

Solving
-7 + -16r + -3r2 = 5

Solving for variable 'r'.

Reorder the terms:
-7 + -5 + -16r + -3r2 = 5 + -5

Combine like terms: -7 + -5 = -12
-12 + -16r + -3r2 = 5 + -5

Combine like terms: 5 + -5 = 0
-12 + -16r + -3r2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 16r + 3r2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(12 + 16r + 3r2)' equal to zero and attempt to solve:

Simplifying
12 + 16r + 3r2 = 0

Solving
12 + 16r + 3r2 = 0

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

Divide each side by '3'.
4 + 5.333333333r + r2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 5.333333333r + -4 + r2 = 0 + -4

Reorder the terms:
4 + -4 + 5.333333333r + r2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5.333333333r + r2 = 0 + -4
5.333333333r + r2 = 0 + -4

Combine like terms: 0 + -4 = -4
5.333333333r + r2 = -4

The r term is 5.333333333r.  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.
5.333333333r + 7.111111113 + r2 = -4 + 7.111111113

Reorder the terms:
7.111111113 + 5.333333333r + r2 = -4 + 7.111111113

Combine like terms: -4 + 7.111111113 = 3.111111113
7.111111113 + 5.333333333r + r2 = 3.111111113

Factor a perfect square on the left side:
(r + 2.666666667)(r + 2.666666667) = 3.111111113

Calculate the square root of the right side: 1.763834208

Break this problem into two subproblems by setting 
(r + 2.666666667) equal to 1.763834208 and -1.763834208.


Subproblem 1
r + 2.666666667 = 1.763834208

Simplifying
r + 2.666666667 = 1.763834208

Reorder the terms:
2.666666667 + r = 1.763834208

Solving
2.666666667 + r = 1.763834208

Solving for variable 'r'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + r = 1.763834208 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + r = 1.763834208 + -2.666666667
r = 1.763834208 + -2.666666667

Combine like terms: 1.763834208 + -2.666666667 = -0.902832459
r = -0.902832459

Simplifying
r = -0.902832459


Subproblem 2
r + 2.666666667 = -1.763834208

Simplifying
r + 2.666666667 = -1.763834208

Reorder the terms:
2.666666667 + r = -1.763834208

Solving
2.666666667 + r = -1.763834208

Solving for variable 'r'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + r = -1.763834208 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + r = -1.763834208 + -2.666666667
r = -1.763834208 + -2.666666667

Combine like terms: -1.763834208 + -2.666666667 = -4.430500875
r = -4.430500875

Simplifying
r = -4.430500875


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.902832459, -4.430500875}
Solution
r = {-0.902832459, -4.430500875}

See similar equations:

| 21x+1=15x+3 | | 15-7x=-32+1x | | 4y+9=2y+13 | | -27=a-13 | | 0=r^2-6.25 | | 160=x(24) | | -52=6x-2x+12 | | y=-16x^2+96x+160 | | 16x^2+40y=4y^2+164 | | 0=r^2-102.01 | | -2x+11y=5 | | n+40=4n+10 | | 5*5x=6y | | 2(x+4)+10=24+x | | 35x-35=20x+10 | | (x+3)(x+5)=x | | 8(x-6)=7(x-2) | | 0=r^2-524.41 | | 8-4c+-6=-4-2(2c-3) | | (4a-5)2=36 | | 87=b+73 | | 2x+24=2/7x | | 2x^2-18x=-3x^2-7x-2 | | 6*x+(500-x)*10= | | 4x+6+5x-3=48 | | 100x+1900y=635 | | -41=b+44 | | (5x+3)(3x^2-14x-5)=0 | | -48=-6(2x-2) | | 50=n-59 | | x+2x-5=25 | | 2sinx=4sinx+6 |

Equations solver categories