2r^2-4r+1=0

Simple and best practice solution for 2r^2-4r+1=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 2r^2-4r+1=0 equation:


Simplifying
2r2 + -4r + 1 = 0

Reorder the terms:
1 + -4r + 2r2 = 0

Solving
1 + -4r + 2r2 = 0

Solving for variable 'r'.

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 = 0.5
1 + -2r + r2 = 0.5

Factor a perfect square on the left side:
(r + -1)(r + -1) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(r + -1) equal to 0.707106781 and -0.707106781.

Subproblem 1

r + -1 = 0.707106781 Simplifying r + -1 = 0.707106781 Reorder the terms: -1 + r = 0.707106781 Solving -1 + r = 0.707106781 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 = 0.707106781 + 1 Combine like terms: -1 + 1 = 0 0 + r = 0.707106781 + 1 r = 0.707106781 + 1 Combine like terms: 0.707106781 + 1 = 1.707106781 r = 1.707106781 Simplifying r = 1.707106781

Subproblem 2

r + -1 = -0.707106781 Simplifying r + -1 = -0.707106781 Reorder the terms: -1 + r = -0.707106781 Solving -1 + r = -0.707106781 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 = -0.707106781 + 1 Combine like terms: -1 + 1 = 0 0 + r = -0.707106781 + 1 r = -0.707106781 + 1 Combine like terms: -0.707106781 + 1 = 0.292893219 r = 0.292893219 Simplifying r = 0.292893219

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.707106781, 0.292893219}

See similar equations:

| 4(-8x+12)=26-32x | | g(x)=x^3-x+1 | | 8.4t=4.2 | | 5(2w-7)=3 | | 4tan(3x)=5 | | ln(x+4)-ln(x-2)=4 | | 1x+5y=124 | | 4+x=3x-20 | | (x-i)(x+i)=0 | | 1/2n+7=n/14/2 | | 3n-5=-8(6-52) | | (8.8)(-0.9)=7.92 | | 3-3(2x+4)=21 | | 9(w^2+1)=-9 | | x^2+22x+837=0 | | Y+9=-12-y+3 | | -2(m+l)=10 | | 3a-5+2a= | | 2(5a-13)=6(-2a+3) | | -16x^2+15x+12=0 | | 199200(2/x)=150x | | 3x+5+x=-1-2x | | -4.3x-2.2x=13 | | Y=10+0.89*100 | | 22x(45+32)56=1000 | | 0.5+0.5x-1.7x=-0.46 | | 0.5+0.5-1.7x=-0.46 | | 1/2x+3=x-4 | | 40=5(10+a) | | 0.99*100=y | | log(6)(13-x)=1 | | 80=-80 |

Equations solver categories