10r^2+20r+17=3

Solution for 10r^2+20r+17=3 equation:

Simplifying
10r2 + 20r + 17 = 3

Reorder the terms:
17 + 20r + 10r2 = 3

Solving
17 + 20r + 10r2 = 3

Solving for variable 'r'.

Reorder the terms:
17 + -3 + 20r + 10r2 = 3 + -3

Combine like terms: 17 + -3 = 14
14 + 20r + 10r2 = 3 + -3

Combine like terms: 3 + -3 = 0
14 + 20r + 10r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 10r + 5r2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + 10r + 5r2)' equal to zero and attempt to solve:

Simplifying
7 + 10r + 5r2 = 0

Solving
7 + 10r + 5r2 = 0

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

Divide each side by '5'.
1.4 + 2r + r2 = 0

Move the constant term to the right:

Add '-1.4' to each side of the equation.
1.4 + 2r + -1.4 + r2 = 0 + -1.4

Reorder the terms:
1.4 + -1.4 + 2r + r2 = 0 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + 2r + r2 = 0 + -1.4
2r + r2 = 0 + -1.4

Combine like terms: 0 + -1.4 = -1.4
2r + r2 = -1.4

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2r + 1 + r2 = -1.4 + 1

Reorder the terms:
1 + 2r + r2 = -1.4 + 1

Combine like terms: -1.4 + 1 = -0.4
1 + 2r + r2 = -0.4

Factor a perfect square on the left side:
(r + 1)(r + 1) = -0.4

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.