6r^2-9r+2=0

Simple and best practice solution for 6r^2-9r+2=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 6r^2-9r+2=0 equation:


Simplifying
6r2 + -9r + 2 = 0

Reorder the terms:
2 + -9r + 6r2 = 0

Solving
2 + -9r + 6r2 = 0

Solving for variable 'r'.

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

Divide each side by '6'.
0.3333333333 + -1.5r + r2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -1.5r + -0.3333333333 + r2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -1.5r + r2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -1.5r + r2 = 0 + -0.3333333333
-1.5r + r2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-1.5r + r2 = -0.3333333333

The r term is -1.5r.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5r + 0.5625 + r2 = -0.3333333333 + 0.5625

Reorder the terms:
0.5625 + -1.5r + r2 = -0.3333333333 + 0.5625

Combine like terms: -0.3333333333 + 0.5625 = 0.2291666667
0.5625 + -1.5r + r2 = 0.2291666667

Factor a perfect square on the left side:
(r + -0.75)(r + -0.75) = 0.2291666667

Calculate the square root of the right side: 0.478713554

Break this problem into two subproblems by setting 
(r + -0.75) equal to 0.478713554 and -0.478713554.

Subproblem 1

r + -0.75 = 0.478713554 Simplifying r + -0.75 = 0.478713554 Reorder the terms: -0.75 + r = 0.478713554 Solving -0.75 + r = 0.478713554 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + r = 0.478713554 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + r = 0.478713554 + 0.75 r = 0.478713554 + 0.75 Combine like terms: 0.478713554 + 0.75 = 1.228713554 r = 1.228713554 Simplifying r = 1.228713554

Subproblem 2

r + -0.75 = -0.478713554 Simplifying r + -0.75 = -0.478713554 Reorder the terms: -0.75 + r = -0.478713554 Solving -0.75 + r = -0.478713554 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + r = -0.478713554 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + r = -0.478713554 + 0.75 r = -0.478713554 + 0.75 Combine like terms: -0.478713554 + 0.75 = 0.271286446 r = 0.271286446 Simplifying r = 0.271286446

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.228713554, 0.271286446}

See similar equations:

| 3e^2+20e-32=0 | | x/-5-1-(-8) | | 2(x-6)(x-9)+2x(x-6)+2x(x-9)=1134 | | 36-12x/4x-12 | | 9x+15-8x=-7-13 | | x^3-6x^2+4=0 | | -17x=493 | | 7d^2+d-8=0 | | (3x^2/4y)*(2y^2/24x^3) | | 1/4x-5/8x=15-24 | | x/3+6=5x-2 | | 0.75=20*log(x) | | 12-(-5)-3+13= | | 23c^2+56c+20=0 | | -5/8x=-15/32 | | 13b^2+58b+24=0 | | 9x+11x-6=0 | | -7/2 | | 5x^2+16x-8=0 | | 14-(-4)-3+13= | | 9+3u=81-15u | | 11a^2+39a+18=0 | | 9x+3=9-bracket(4x-5) | | 5/6t=-8/9 | | 4(2a-b)-6(3b-7a)= | | (5x^2)+(7x^3)+(9x^4)=0 | | 2z^2+19z+42=0 | | log(2x)=log(x+5) | | 9x^2+12x+144=0 | | 4(3x-6)=12x-24 | | 2/2×5/10 | | y=6x^3+3x+1 |

Equations solver categories