9r^2+6r=1

Simple and best practice solution for 9r^2+6r=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 9r^2+6r=1 equation:


Simplifying
9r2 + 6r = 1

Reorder the terms:
6r + 9r2 = 1

Solving
6r + 9r2 = 1

Solving for variable 'r'.

Reorder the terms:
-1 + 6r + 9r2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 6r + 9r2 = 0

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

Divide each side by '9'.
-0.1111111111 + 0.6666666667r + r2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + 0.6666666667r + 0.1111111111 + r2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + 0.6666666667r + r2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + 0.6666666667r + r2 = 0 + 0.1111111111
0.6666666667r + r2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
0.6666666667r + r2 = 0.1111111111

The r term is 0.6666666667r.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667r + 0.1111111112 + r2 = 0.1111111111 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667r + r2 = 0.1111111111 + 0.1111111112

Combine like terms: 0.1111111111 + 0.1111111112 = 0.2222222223
0.1111111112 + 0.6666666667r + r2 = 0.2222222223

Factor a perfect square on the left side:
(r + 0.3333333334)(r + 0.3333333334) = 0.2222222223

Calculate the square root of the right side: 0.471404521

Break this problem into two subproblems by setting 
(r + 0.3333333334) equal to 0.471404521 and -0.471404521.

Subproblem 1

r + 0.3333333334 = 0.471404521 Simplifying r + 0.3333333334 = 0.471404521 Reorder the terms: 0.3333333334 + r = 0.471404521 Solving 0.3333333334 + r = 0.471404521 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + r = 0.471404521 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + r = 0.471404521 + -0.3333333334 r = 0.471404521 + -0.3333333334 Combine like terms: 0.471404521 + -0.3333333334 = 0.1380711876 r = 0.1380711876 Simplifying r = 0.1380711876

Subproblem 2

r + 0.3333333334 = -0.471404521 Simplifying r + 0.3333333334 = -0.471404521 Reorder the terms: 0.3333333334 + r = -0.471404521 Solving 0.3333333334 + r = -0.471404521 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + r = -0.471404521 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + r = -0.471404521 + -0.3333333334 r = -0.471404521 + -0.3333333334 Combine like terms: -0.471404521 + -0.3333333334 = -0.8047378544 r = -0.8047378544 Simplifying r = -0.8047378544

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.1380711876, -0.8047378544}

See similar equations:

| 5(4x-6)-(3x+3)= | | 3x+28=10-28 | | N+43=54 | | x^2-15x-25= | | 1/16(50)^2-(y-28)^2=0 | | 2x+19=11x-7 | | 3-6x=8-6x | | y+y+10+2y-10=180 | | 3r-6t=ar+2 | | 8x-28=4x+5 | | 3x+11=60-40 | | 9x^2+9y^2=135 | | 5x*(x+7)-5=0 | | 2x^2+23x+30=154 | | 2x^2+23x=154 | | 2x^2+23x=124 | | x^2-5x-2.75=0 | | 12x-42=5x+14 | | Y^4-12y^2+32=0 | | f(x)=2x^2-8x+5 | | x^2+16x-41=0 | | -24=y/4 | | g/5=-13 | | 3/x+4x/x-3=4 | | 9x+14=(x-13) | | p+2p=3 | | x^2+8-1=19 | | ((t^2-9)/(t+3))*(4/16t) | | 3(4c-1)-5=8c+8 | | 7x-49y=14 | | 16=2(q+4)+3 | | 3a^2+18a-7=0 |

Equations solver categories