5r^2+84r-80=0

Simple and best practice solution for 5r^2+84r-80=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 5r^2+84r-80=0 equation:


Simplifying
5r2 + 84r + -80 = 0

Reorder the terms:
-80 + 84r + 5r2 = 0

Solving
-80 + 84r + 5r2 = 0

Solving for variable 'r'.

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

Divide each side by '5'.
-16 + 16.8r + r2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 16.8r + 16 + r2 = 0 + 16

Reorder the terms:
-16 + 16 + 16.8r + r2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 16.8r + r2 = 0 + 16
16.8r + r2 = 0 + 16

Combine like terms: 0 + 16 = 16
16.8r + r2 = 16

The r term is 16.8r.  Take half its coefficient (8.4).
Square it (70.56) and add it to both sides.

Add '70.56' to each side of the equation.
16.8r + 70.56 + r2 = 16 + 70.56

Reorder the terms:
70.56 + 16.8r + r2 = 16 + 70.56

Combine like terms: 16 + 70.56 = 86.56
70.56 + 16.8r + r2 = 86.56

Factor a perfect square on the left side:
(r + 8.4)(r + 8.4) = 86.56

Calculate the square root of the right side: 9.30376268

Break this problem into two subproblems by setting 
(r + 8.4) equal to 9.30376268 and -9.30376268.

Subproblem 1

r + 8.4 = 9.30376268 Simplifying r + 8.4 = 9.30376268 Reorder the terms: 8.4 + r = 9.30376268 Solving 8.4 + r = 9.30376268 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.4' to each side of the equation. 8.4 + -8.4 + r = 9.30376268 + -8.4 Combine like terms: 8.4 + -8.4 = 0.0 0.0 + r = 9.30376268 + -8.4 r = 9.30376268 + -8.4 Combine like terms: 9.30376268 + -8.4 = 0.90376268 r = 0.90376268 Simplifying r = 0.90376268

Subproblem 2

r + 8.4 = -9.30376268 Simplifying r + 8.4 = -9.30376268 Reorder the terms: 8.4 + r = -9.30376268 Solving 8.4 + r = -9.30376268 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8.4' to each side of the equation. 8.4 + -8.4 + r = -9.30376268 + -8.4 Combine like terms: 8.4 + -8.4 = 0.0 0.0 + r = -9.30376268 + -8.4 r = -9.30376268 + -8.4 Combine like terms: -9.30376268 + -8.4 = -17.70376268 r = -17.70376268 Simplifying r = -17.70376268

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.90376268, -17.70376268}

See similar equations:

| x+4=-4x-11 | | 11=1-2n-8n | | 3h+8=h-2 | | 2(1/2q+1) | | 6*x^2-7x-3=0 | | y=(-2)-8 | | m/8=8-1/3 | | -5x-2=x+22 | | 38m-18=96 | | 1/2(-4+6x)=1/3x+2/3(x+9) | | 28-x=180 | | 7a^2-112= | | 16=6m-4m | | 4*x^2+16x+15=0 | | x(28-x)=180 | | 6g-1=-g+20 | | 2x+84=6x+40 | | -2k-3=16 | | y=2/x | | 5n^2+41n+42=0 | | 4/5(2+m)=24 | | 18=16-4(x+7)-2x | | x^2+12x-27=2x-3 | | -5x-3=-x-11 | | 0.8x(-7)= | | 2x+(-2)=-4 | | -2(p-5)+7p=-3 | | 18=-3(m-6) | | 3a-2b=8 | | X^2+11=3x | | -17+25-14= | | 12x+4=12x-8 |

Equations solver categories