(r-5)(r-5)=-3

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Solution for (r-5)(r-5)=-3 equation:


Simplifying
(r + -5)(r + -5) = -3

Reorder the terms:
(-5 + r)(r + -5) = -3

Reorder the terms:
(-5 + r)(-5 + r) = -3

Multiply (-5 + r) * (-5 + r)
(-5(-5 + r) + r(-5 + r)) = -3
((-5 * -5 + r * -5) + r(-5 + r)) = -3
((25 + -5r) + r(-5 + r)) = -3
(25 + -5r + (-5 * r + r * r)) = -3
(25 + -5r + (-5r + r2)) = -3

Combine like terms: -5r + -5r = -10r
(25 + -10r + r2) = -3

Solving
25 + -10r + r2 = -3

Solving for variable 'r'.

Reorder the terms:
25 + 3 + -10r + r2 = -3 + 3

Combine like terms: 25 + 3 = 28
28 + -10r + r2 = -3 + 3

Combine like terms: -3 + 3 = 0
28 + -10r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -10r + -28 + r2 = 0 + -28

Reorder the terms:
28 + -28 + -10r + r2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -10r + r2 = 0 + -28
-10r + r2 = 0 + -28

Combine like terms: 0 + -28 = -28
-10r + r2 = -28

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 = -28 + 25

Reorder the terms:
25 + -10r + r2 = -28 + 25

Combine like terms: -28 + 25 = -3
25 + -10r + r2 = -3

Factor a perfect square on the left side:
(r + -5)(r + -5) = -3

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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