40r^2-100r+250=0

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Solution for 40r^2-100r+250=0 equation: 


Simplifying
40r2 + -100r + 250 = 0

Reorder the terms:
250 + -100r + 40r2 = 0

Solving
250 + -100r + 40r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '10'.
10(25 + -10r + 4r2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(25 + -10r + 4r2)' equal to zero and attempt to solve:

Simplifying
25 + -10r + 4r2 = 0

Solving
25 + -10r + 4r2 = 0

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

Divide each side by '4'.
6.25 + -2.5r + r2 = 0

Move the constant term to the right:

Add '-6.25' to each side of the equation.
6.25 + -2.5r + -6.25 + r2 = 0 + -6.25

Reorder the terms:
6.25 + -6.25 + -2.5r + r2 = 0 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + -2.5r + r2 = 0 + -6.25
-2.5r + r2 = 0 + -6.25

Combine like terms: 0 + -6.25 = -6.25
-2.5r + r2 = -6.25

The r term is -2.5r.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5r + 1.5625 + r2 = -6.25 + 1.5625

Reorder the terms:
1.5625 + -2.5r + r2 = -6.25 + 1.5625

Combine like terms: -6.25 + 1.5625 = -4.6875
1.5625 + -2.5r + r2 = -4.6875

Factor a perfect square on the left side:
(r + -1.25)(r + -1.25) = -4.6875

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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