6r^2-5r=7

Simple and best practice solution for 6r^2-5r=7 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^2-5r=7 equation:


Simplifying
6r2 + -5r = 7

Reorder the terms:
-5r + 6r2 = 7

Solving
-5r + 6r2 = 7

Solving for variable 'r'.

Reorder the terms:
-7 + -5r + 6r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -5r + 6r2 = 0

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

Divide each side by '6'.
-1.166666667 + -0.8333333333r + r2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + -0.8333333333r + 1.166666667 + r2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + -0.8333333333r + r2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + -0.8333333333r + r2 = 0 + 1.166666667
-0.8333333333r + r2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
-0.8333333333r + r2 = 1.166666667

The r term is -0.8333333333r.  Take half its coefficient (-0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
-0.8333333333r + 0.1736111111 + r2 = 1.166666667 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333r + r2 = 1.166666667 + 0.1736111111

Combine like terms: 1.166666667 + 0.1736111111 = 1.3402777781
0.1736111111 + -0.8333333333r + r2 = 1.3402777781

Factor a perfect square on the left side:
(r + -0.4166666667)(r + -0.4166666667) = 1.3402777781

Calculate the square root of the right side: 1.157703666

Break this problem into two subproblems by setting 
(r + -0.4166666667) equal to 1.157703666 and -1.157703666.

Subproblem 1

r + -0.4166666667 = 1.157703666 Simplifying r + -0.4166666667 = 1.157703666 Reorder the terms: -0.4166666667 + r = 1.157703666 Solving -0.4166666667 + r = 1.157703666 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + r = 1.157703666 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + r = 1.157703666 + 0.4166666667 r = 1.157703666 + 0.4166666667 Combine like terms: 1.157703666 + 0.4166666667 = 1.5743703327 r = 1.5743703327 Simplifying r = 1.5743703327

Subproblem 2

r + -0.4166666667 = -1.157703666 Simplifying r + -0.4166666667 = -1.157703666 Reorder the terms: -0.4166666667 + r = -1.157703666 Solving -0.4166666667 + r = -1.157703666 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + r = -1.157703666 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + r = -1.157703666 + 0.4166666667 r = -1.157703666 + 0.4166666667 Combine like terms: -1.157703666 + 0.4166666667 = -0.7410369993 r = -0.7410369993 Simplifying r = -0.7410369993

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.5743703327, -0.7410369993}

See similar equations:

| 7(v+1)-3=3v-16 | | 7.36d=29.4 | | 29+x=17.25 | | (6x+2)+(3x+1)= | | 3-(7-8b)=12b+-5(3b+-8) | | 16z+86=z | | 5w-8w=-21 | | 7[4n+2]-8= | | y+23=2y | | 2(x-3)-7=28-5(x+4) | | 20s-26=6s+30 | | 8m-15=7-m | | (.1x+.8)-(.066x-.33)=1 | | 11x+4-5y=9 | | 4(6-x)=2 | | 11x^2=8x+120 | | 6(a+5)=36 | | 4u-26=u | | a+14=4a+5 | | x^2-8x=35+b^2 | | 10/m-9/n | | 4x^3+18x^2+26x+10=0 | | x^2-8x+65=100+b^2 | | -13n+18=-12-13 | | 2log[5](x+2)=log[5](x+8) | | -7(4)=21 | | 61=c-15 | | 9=14cosx | | (-1)(4i)=0 | | 2x-13=-5x-2 | | 3a+43=9a+1 | | 3c+83=8c+18 |

Equations solver categories