-7r^2+140r-75=0

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Solution for -7r^2+140r-75=0 equation: 


Simplifying
-7r2 + 140r + -75 = 0

Reorder the terms:
-75 + 140r + -7r2 = 0

Solving
-75 + 140r + -7r2 = 0

Solving for variable 'r'.

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

Divide each side by '-7'.
10.71428571 + -20r + r2 = 0

Move the constant term to the right:

Add '-10.71428571' to each side of the equation.
10.71428571 + -20r + -10.71428571 + r2 = 0 + -10.71428571

Reorder the terms:
10.71428571 + -10.71428571 + -20r + r2 = 0 + -10.71428571

Combine like terms: 10.71428571 + -10.71428571 = 0.00000000
0.00000000 + -20r + r2 = 0 + -10.71428571
-20r + r2 = 0 + -10.71428571

Combine like terms: 0 + -10.71428571 = -10.71428571
-20r + r2 = -10.71428571

The r term is -20r.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20r + 100 + r2 = -10.71428571 + 100

Reorder the terms:
100 + -20r + r2 = -10.71428571 + 100

Combine like terms: -10.71428571 + 100 = 89.28571429
100 + -20r + r2 = 89.28571429

Factor a perfect square on the left side:
(r + -10)(r + -10) = 89.28571429

Calculate the square root of the right side: 9.449111825

Break this problem into two subproblems by setting 
(r + -10) equal to 9.449111825 and -9.449111825.


Subproblem 1
r + -10 = 9.449111825

Simplifying
r + -10 = 9.449111825

Reorder the terms:
-10 + r = 9.449111825

Solving
-10 + r = 9.449111825

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + r = 9.449111825 + 10

Combine like terms: -10 + 10 = 0
0 + r = 9.449111825 + 10
r = 9.449111825 + 10

Combine like terms: 9.449111825 + 10 = 19.449111825
r = 19.449111825

Simplifying
r = 19.449111825


Subproblem 2
r + -10 = -9.449111825

Simplifying
r + -10 = -9.449111825

Reorder the terms:
-10 + r = -9.449111825

Solving
-10 + r = -9.449111825

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + r = -9.449111825 + 10

Combine like terms: -10 + 10 = 0
0 + r = -9.449111825 + 10
r = -9.449111825 + 10

Combine like terms: -9.449111825 + 10 = 0.550888175
r = 0.550888175

Simplifying
r = 0.550888175


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {19.449111825, 0.550888175}

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