7r^2+140r-700=0

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Solution for 7r^2+140r-700=0 equation: 


Simplifying
7r2 + 140r + -700 = 0

Reorder the terms:
-700 + 140r + 7r2 = 0

Solving
-700 + 140r + 7r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-100 + 20r + r2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-100 + 20r + r2)' equal to zero and attempt to solve:

Simplifying
-100 + 20r + r2 = 0

Solving
-100 + 20r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 20r + 100 + r2 = 0 + 100

Reorder the terms:
-100 + 100 + 20r + r2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 20r + r2 = 0 + 100
20r + r2 = 0 + 100

Combine like terms: 0 + 100 = 100
20r + r2 = 100

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 = 100 + 100

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

Combine like terms: 100 + 100 = 200
100 + 20r + r2 = 200

Factor a perfect square on the left side:
(r + 10)(r + 10) = 200

Calculate the square root of the right side: 14.142135624

Break this problem into two subproblems by setting 
(r + 10) equal to 14.142135624 and -14.142135624.


Subproblem 1
r + 10 = 14.142135624

Simplifying
r + 10 = 14.142135624

Reorder the terms:
10 + r = 14.142135624

Solving
10 + r = 14.142135624

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 = 14.142135624 + -10

Combine like terms: 10 + -10 = 0
0 + r = 14.142135624 + -10
r = 14.142135624 + -10

Combine like terms: 14.142135624 + -10 = 4.142135624
r = 4.142135624

Simplifying
r = 4.142135624


Subproblem 2
r + 10 = -14.142135624

Simplifying
r + 10 = -14.142135624

Reorder the terms:
10 + r = -14.142135624

Solving
10 + r = -14.142135624

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 = -14.142135624 + -10

Combine like terms: 10 + -10 = 0
0 + r = -14.142135624 + -10
r = -14.142135624 + -10

Combine like terms: -14.142135624 + -10 = -24.142135624
r = -24.142135624

Simplifying
r = -24.142135624


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.142135624, -24.142135624}
Solution
r = {4.142135624, -24.142135624}

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