10r^2+76r+140=0

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Solution for 10r^2+76r+140=0 equation: 


Simplifying
10r2 + 76r + 140 = 0

Reorder the terms:
140 + 76r + 10r2 = 0

Solving
140 + 76r + 10r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(70 + 38r + 5r2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(70 + 38r + 5r2)' equal to zero and attempt to solve:

Simplifying
70 + 38r + 5r2 = 0

Solving
70 + 38r + 5r2 = 0

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

Divide each side by '5'.
14 + 7.6r + r2 = 0

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 7.6r + -14 + r2 = 0 + -14

Reorder the terms:
14 + -14 + 7.6r + r2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 7.6r + r2 = 0 + -14
7.6r + r2 = 0 + -14

Combine like terms: 0 + -14 = -14
7.6r + r2 = -14

The r term is 7.6r.  Take half its coefficient (3.8).
Square it (14.44) and add it to both sides.

Add '14.44' to each side of the equation.
7.6r + 14.44 + r2 = -14 + 14.44

Reorder the terms:
14.44 + 7.6r + r2 = -14 + 14.44

Combine like terms: -14 + 14.44 = 0.44
14.44 + 7.6r + r2 = 0.44

Factor a perfect square on the left side:
(r + 3.8)(r + 3.8) = 0.44

Calculate the square root of the right side: 0.663324958

Break this problem into two subproblems by setting 
(r + 3.8) equal to 0.663324958 and -0.663324958.


Subproblem 1
r + 3.8 = 0.663324958

Simplifying
r + 3.8 = 0.663324958

Reorder the terms:
3.8 + r = 0.663324958

Solving
3.8 + r = 0.663324958

Solving for variable 'r'.

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

Add '-3.8' to each side of the equation.
3.8 + -3.8 + r = 0.663324958 + -3.8

Combine like terms: 3.8 + -3.8 = 0.0
0.0 + r = 0.663324958 + -3.8
r = 0.663324958 + -3.8

Combine like terms: 0.663324958 + -3.8 = -3.136675042
r = -3.136675042

Simplifying
r = -3.136675042


Subproblem 2
r + 3.8 = -0.663324958

Simplifying
r + 3.8 = -0.663324958

Reorder the terms:
3.8 + r = -0.663324958

Solving
3.8 + r = -0.663324958

Solving for variable 'r'.

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

Add '-3.8' to each side of the equation.
3.8 + -3.8 + r = -0.663324958 + -3.8

Combine like terms: 3.8 + -3.8 = 0.0
0.0 + r = -0.663324958 + -3.8
r = -0.663324958 + -3.8

Combine like terms: -0.663324958 + -3.8 = -4.463324958
r = -4.463324958

Simplifying
r = -4.463324958


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-3.136675042, -4.463324958}
Solution
r = {-3.136675042, -4.463324958}

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