r^2-7r+4=0

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Solution for r^2-7r+4=0 equation: 


Simplifying
r2 + -7r + 4 = 0

Reorder the terms:
4 + -7r + r2 = 0

Solving
4 + -7r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -7r + -4 + r2 = 0 + -4

Reorder the terms:
4 + -4 + -7r + r2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7r + r2 = 0 + -4
-7r + r2 = 0 + -4

Combine like terms: 0 + -4 = -4
-7r + r2 = -4

The r term is -7r.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7r + 12.25 + r2 = -4 + 12.25

Reorder the terms:
12.25 + -7r + r2 = -4 + 12.25

Combine like terms: -4 + 12.25 = 8.25
12.25 + -7r + r2 = 8.25

Factor a perfect square on the left side:
(r + -3.5)(r + -3.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(r + -3.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
r + -3.5 = 2.872281323

Simplifying
r + -3.5 = 2.872281323

Reorder the terms:
-3.5 + r = 2.872281323

Solving
-3.5 + r = 2.872281323

Solving for variable 'r'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + r = 2.872281323 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + r = 2.872281323 + 3.5
r = 2.872281323 + 3.5

Combine like terms: 2.872281323 + 3.5 = 6.372281323
r = 6.372281323

Simplifying
r = 6.372281323


Subproblem 2
r + -3.5 = -2.872281323

Simplifying
r + -3.5 = -2.872281323

Reorder the terms:
-3.5 + r = -2.872281323

Solving
-3.5 + r = -2.872281323

Solving for variable 'r'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + r = -2.872281323 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + r = -2.872281323 + 3.5
r = -2.872281323 + 3.5

Combine like terms: -2.872281323 + 3.5 = 0.627718677
r = 0.627718677

Simplifying
r = 0.627718677


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {6.372281323, 0.627718677}

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