7(r-5)r=2

Simple and best practice solution for 7(r-5)r=2 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 7(r-5)r=2 equation:


Simplifying
7(r + -5) * r = 2

Reorder the terms:
7(-5 + r) * r = 2

Reorder the terms for easier multiplication:
7r(-5 + r) = 2
(-5 * 7r + r * 7r) = 2
(-35r + 7r2) = 2

Solving
-35r + 7r2 = 2

Solving for variable 'r'.

Reorder the terms:
-2 + -35r + 7r2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -35r + 7r2 = 0

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

Divide each side by '7'.
-0.2857142857 + -5r + r2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + -5r + 0.2857142857 + r2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + -5r + r2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + -5r + r2 = 0 + 0.2857142857
-5r + r2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
-5r + r2 = 0.2857142857

The r term is -5r.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5r + 6.25 + r2 = 0.2857142857 + 6.25

Reorder the terms:
6.25 + -5r + r2 = 0.2857142857 + 6.25

Combine like terms: 0.2857142857 + 6.25 = 6.5357142857
6.25 + -5r + r2 = 6.5357142857

Factor a perfect square on the left side:
(r + -2.5)(r + -2.5) = 6.5357142857

Calculate the square root of the right side: 2.55650431

Break this problem into two subproblems by setting 
(r + -2.5) equal to 2.55650431 and -2.55650431.

Subproblem 1

r + -2.5 = 2.55650431 Simplifying r + -2.5 = 2.55650431 Reorder the terms: -2.5 + r = 2.55650431 Solving -2.5 + r = 2.55650431 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + r = 2.55650431 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + r = 2.55650431 + 2.5 r = 2.55650431 + 2.5 Combine like terms: 2.55650431 + 2.5 = 5.05650431 r = 5.05650431 Simplifying r = 5.05650431

Subproblem 2

r + -2.5 = -2.55650431 Simplifying r + -2.5 = -2.55650431 Reorder the terms: -2.5 + r = -2.55650431 Solving -2.5 + r = -2.55650431 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + r = -2.55650431 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + r = -2.55650431 + 2.5 r = -2.55650431 + 2.5 Combine like terms: -2.55650431 + 2.5 = -0.05650431 r = -0.05650431 Simplifying r = -0.05650431

Solution

The solution to the problem is based on the solutions from the subproblems. r = {5.05650431, -0.05650431}

See similar equations:

| -5x=36+7x | | -1.6= | | 6x^3-22x^2-20x=0 | | 11-3x=3+x | | 6d^2+21d=10d+25 | | (2k+8)/4=3 | | -12=2x+1 | | x^2+17x-7=0 | | 10y=9y-1.4 | | -5+16=6b-2-5b | | -12-1= | | x*2-3x-10=0 | | 2q-8q=1 | | 2k+8/4=3 | | 24-x+36=54 | | 7x^2-4=100 | | (C+9)(7c^2+2)=0 | | 0.25d=75 | | x+9x=-9 | | 27X^2-19X=0 | | 76=19y | | (5x+2)(x-4)=0 | | 3p+4q=29 | | 2(t+4)-5t=29-13t | | 2x+12=2x-24 | | 11s+6t=67 | | 3s+2t=19 | | (5x+6)=0 | | 5p+8q=31 | | (5x+6)(x-5)=0 | | 2p+4q=14 | | 15-2x+10x= |

Equations solver categories