r^2-16r+21=4

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Solution for r^2-16r+21=4 equation:


Simplifying
r2 + -16r + 21 = 4

Reorder the terms:
21 + -16r + r2 = 4

Solving
21 + -16r + r2 = 4

Solving for variable 'r'.

Reorder the terms:
21 + -4 + -16r + r2 = 4 + -4

Combine like terms: 21 + -4 = 17
17 + -16r + r2 = 4 + -4

Combine like terms: 4 + -4 = 0
17 + -16r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -16r + -17 + r2 = 0 + -17

Reorder the terms:
17 + -17 + -16r + r2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -16r + r2 = 0 + -17
-16r + r2 = 0 + -17

Combine like terms: 0 + -17 = -17
-16r + r2 = -17

The r term is -16r.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16r + 64 + r2 = -17 + 64

Reorder the terms:
64 + -16r + r2 = -17 + 64

Combine like terms: -17 + 64 = 47
64 + -16r + r2 = 47

Factor a perfect square on the left side:
(r + -8)(r + -8) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(r + -8) equal to 6.8556546 and -6.8556546.

Subproblem 1

r + -8 = 6.8556546 Simplifying r + -8 = 6.8556546 Reorder the terms: -8 + r = 6.8556546 Solving -8 + r = 6.8556546 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + r = 6.8556546 + 8 Combine like terms: -8 + 8 = 0 0 + r = 6.8556546 + 8 r = 6.8556546 + 8 Combine like terms: 6.8556546 + 8 = 14.8556546 r = 14.8556546 Simplifying r = 14.8556546

Subproblem 2

r + -8 = -6.8556546 Simplifying r + -8 = -6.8556546 Reorder the terms: -8 + r = -6.8556546 Solving -8 + r = -6.8556546 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + r = -6.8556546 + 8 Combine like terms: -8 + 8 = 0 0 + r = -6.8556546 + 8 r = -6.8556546 + 8 Combine like terms: -6.8556546 + 8 = 1.1443454 r = 1.1443454 Simplifying r = 1.1443454

Solution

The solution to the problem is based on the solutions from the subproblems. r = {14.8556546, 1.1443454}

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