2r^2-4r=1

Simple and best practice solution for 2r^2-4r=1 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 2r^2-4r=1 equation:


Simplifying
2r2 + -4r = 1

Reorder the terms:
-4r + 2r2 = 1

Solving
-4r + 2r2 = 1

Solving for variable 'r'.

Reorder the terms:
-1 + -4r + 2r2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -4r + 2r2 = 0

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

Divide each side by '2'.
-0.5 + -2r + r2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -2r + 0.5 + r2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -2r + r2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -2r + r2 = 0 + 0.5
-2r + r2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-2r + r2 = 0.5

The r term is -2r.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2r + 1 + r2 = 0.5 + 1

Reorder the terms:
1 + -2r + r2 = 0.5 + 1

Combine like terms: 0.5 + 1 = 1.5
1 + -2r + r2 = 1.5

Factor a perfect square on the left side:
(r + -1)(r + -1) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(r + -1) equal to 1.224744871 and -1.224744871.

Subproblem 1

r + -1 = 1.224744871 Simplifying r + -1 = 1.224744871 Reorder the terms: -1 + r = 1.224744871 Solving -1 + r = 1.224744871 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = 1.224744871 + 1 Combine like terms: -1 + 1 = 0 0 + r = 1.224744871 + 1 r = 1.224744871 + 1 Combine like terms: 1.224744871 + 1 = 2.224744871 r = 2.224744871 Simplifying r = 2.224744871

Subproblem 2

r + -1 = -1.224744871 Simplifying r + -1 = -1.224744871 Reorder the terms: -1 + r = -1.224744871 Solving -1 + r = -1.224744871 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = -1.224744871 + 1 Combine like terms: -1 + 1 = 0 0 + r = -1.224744871 + 1 r = -1.224744871 + 1 Combine like terms: -1.224744871 + 1 = -0.224744871 r = -0.224744871 Simplifying r = -0.224744871

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.224744871, -0.224744871}

See similar equations:

| 8x-12=3x-29 | | 5-5x-6=9 | | 800x-0.49=400x+0.15 | | 10n+2=12 | | (3+5i)(3-5i)=0 | | 12x^2-29x+14=0 | | 8x-12+3x-28=180 | | y=8x^2+16x+9 | | 3.8x-39=2.6x+3 | | 8*1.5*x=144 | | 2w^2+w=6 | | 5.75x+5=30 | | 4x^2+64y^2=256 | | 9x^4+18x^3+27x^2= | | 7.2=5x+9.8 | | x-2=28.5 | | -30-x+x^2= | | p(5π/3) | | y+30=12y-4 | | f(n)=6n-5 | | 75y^4-12y^2= | | an=2n-2 | | t^3+2t^2-9t-18=0 | | x^2+12+7x= | | ln(x-7)=2 | | 48y^4-75y= | | 10x-4/6=11 | | 3m+15=60 | | 105/2(3-x/3)=315 | | s^2-3s-10= | | x^2+5jx+4=y | | 0=-5 |

Equations solver categories