r^2-20r+74=-4

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Solution for r^2-20r+74=-4 equation:


Simplifying
r2 + -20r + 74 = -4

Reorder the terms:
74 + -20r + r2 = -4

Solving
74 + -20r + r2 = -4

Solving for variable 'r'.

Reorder the terms:
74 + 4 + -20r + r2 = -4 + 4

Combine like terms: 74 + 4 = 78
78 + -20r + r2 = -4 + 4

Combine like terms: -4 + 4 = 0
78 + -20r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-78' to each side of the equation.
78 + -20r + -78 + r2 = 0 + -78

Reorder the terms:
78 + -78 + -20r + r2 = 0 + -78

Combine like terms: 78 + -78 = 0
0 + -20r + r2 = 0 + -78
-20r + r2 = 0 + -78

Combine like terms: 0 + -78 = -78
-20r + r2 = -78

The r term is -20r.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20r + 100 + r2 = -78 + 100

Reorder the terms:
100 + -20r + r2 = -78 + 100

Combine like terms: -78 + 100 = 22
100 + -20r + r2 = 22

Factor a perfect square on the left side:
(r + -10)(r + -10) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(r + -10) equal to 4.69041576 and -4.69041576.

Subproblem 1

r + -10 = 4.69041576 Simplifying r + -10 = 4.69041576 Reorder the terms: -10 + r = 4.69041576 Solving -10 + r = 4.69041576 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + r = 4.69041576 + 10 Combine like terms: -10 + 10 = 0 0 + r = 4.69041576 + 10 r = 4.69041576 + 10 Combine like terms: 4.69041576 + 10 = 14.69041576 r = 14.69041576 Simplifying r = 14.69041576

Subproblem 2

r + -10 = -4.69041576 Simplifying r + -10 = -4.69041576 Reorder the terms: -10 + r = -4.69041576 Solving -10 + r = -4.69041576 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + r = -4.69041576 + 10 Combine like terms: -10 + 10 = 0 0 + r = -4.69041576 + 10 r = -4.69041576 + 10 Combine like terms: -4.69041576 + 10 = 5.30958424 r = 5.30958424 Simplifying r = 5.30958424

Solution

The solution to the problem is based on the solutions from the subproblems. r = {14.69041576, 5.30958424}

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