r^2-7r+8=0

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Solution for r^2-7r+8=0 equation:


Simplifying
r2 + -7r + 8 = 0

Reorder the terms:
8 + -7r + r2 = 0

Solving
8 + -7r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -7r + -8 + r2 = 0 + -8

Reorder the terms:
8 + -8 + -7r + r2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7r + r2 = 0 + -8
-7r + r2 = 0 + -8

Combine like terms: 0 + -8 = -8
-7r + r2 = -8

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 = -8 + 12.25

Reorder the terms:
12.25 + -7r + r2 = -8 + 12.25

Combine like terms: -8 + 12.25 = 4.25
12.25 + -7r + r2 = 4.25

Factor a perfect square on the left side:
(r + -3.5)(r + -3.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(r + -3.5) equal to 2.061552813 and -2.061552813.

Subproblem 1

r + -3.5 = 2.061552813 Simplifying r + -3.5 = 2.061552813 Reorder the terms: -3.5 + r = 2.061552813 Solving -3.5 + r = 2.061552813 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 = 2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = 2.061552813 + 3.5 r = 2.061552813 + 3.5 Combine like terms: 2.061552813 + 3.5 = 5.561552813 r = 5.561552813 Simplifying r = 5.561552813

Subproblem 2

r + -3.5 = -2.061552813 Simplifying r + -3.5 = -2.061552813 Reorder the terms: -3.5 + r = -2.061552813 Solving -3.5 + r = -2.061552813 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 = -2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + r = -2.061552813 + 3.5 r = -2.061552813 + 3.5 Combine like terms: -2.061552813 + 3.5 = 1.438447187 r = 1.438447187 Simplifying r = 1.438447187

Solution

The solution to the problem is based on the solutions from the subproblems. r = {5.561552813, 1.438447187}

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