10r+70+49-r^2=169

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Solution for 10r+70+49-r^2=169 equation:


Simplifying
10r + 70 + 49 + -1r2 = 169

Reorder the terms:
70 + 49 + 10r + -1r2 = 169

Combine like terms: 70 + 49 = 119
119 + 10r + -1r2 = 169

Solving
119 + 10r + -1r2 = 169

Solving for variable 'r'.

Reorder the terms:
119 + -169 + 10r + -1r2 = 169 + -169

Combine like terms: 119 + -169 = -50
-50 + 10r + -1r2 = 169 + -169

Combine like terms: 169 + -169 = 0
-50 + 10r + -1r2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
50 + -10r + r2 = 0

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + -10r + -50 + r2 = 0 + -50

Reorder the terms:
50 + -50 + -10r + r2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -10r + r2 = 0 + -50
-10r + r2 = 0 + -50

Combine like terms: 0 + -50 = -50
-10r + r2 = -50

The r term is -10r.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10r + 25 + r2 = -50 + 25

Reorder the terms:
25 + -10r + r2 = -50 + 25

Combine like terms: -50 + 25 = -25
25 + -10r + r2 = -25

Factor a perfect square on the left side:
(r + -5)(r + -5) = -25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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