r^2+5r-42=0

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Solution for r^2+5r-42=0 equation: 


Simplifying
r2 + 5r + -42 = 0

Reorder the terms:
-42 + 5r + r2 = 0

Solving
-42 + 5r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + 5r + 42 + r2 = 0 + 42

Reorder the terms:
-42 + 42 + 5r + r2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 5r + r2 = 0 + 42
5r + r2 = 0 + 42

Combine like terms: 0 + 42 = 42
5r + r2 = 42

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 = 42 + 6.25

Reorder the terms:
6.25 + 5r + r2 = 42 + 6.25

Combine like terms: 42 + 6.25 = 48.25
6.25 + 5r + r2 = 48.25

Factor a perfect square on the left side:
(r + 2.5)(r + 2.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(r + 2.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
r + 2.5 = 6.946221995

Simplifying
r + 2.5 = 6.946221995

Reorder the terms:
2.5 + r = 6.946221995

Solving
2.5 + r = 6.946221995

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 = 6.946221995 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + r = 6.946221995 + -2.5
r = 6.946221995 + -2.5

Combine like terms: 6.946221995 + -2.5 = 4.446221995
r = 4.446221995

Simplifying
r = 4.446221995


Subproblem 2
r + 2.5 = -6.946221995

Simplifying
r + 2.5 = -6.946221995

Reorder the terms:
2.5 + r = -6.946221995

Solving
2.5 + r = -6.946221995

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 = -6.946221995 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + r = -6.946221995 + -2.5
r = -6.946221995 + -2.5

Combine like terms: -6.946221995 + -2.5 = -9.446221995
r = -9.446221995

Simplifying
r = -9.446221995


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.446221995, -9.446221995}

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