3r^2+7r+40=0

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Solution for 3r^2+7r+40=0 equation:


Simplifying
3r2 + 7r + 40 = 0

Reorder the terms:
40 + 7r + 3r2 = 0

Solving
40 + 7r + 3r2 = 0

Solving for variable 'r'.

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

Divide each side by '3'.
13.33333333 + 2.333333333r + r2 = 0

Move the constant term to the right:

Add '-13.33333333' to each side of the equation.
13.33333333 + 2.333333333r + -13.33333333 + r2 = 0 + -13.33333333

Reorder the terms:
13.33333333 + -13.33333333 + 2.333333333r + r2 = 0 + -13.33333333

Combine like terms: 13.33333333 + -13.33333333 = 0.00000000
0.00000000 + 2.333333333r + r2 = 0 + -13.33333333
2.333333333r + r2 = 0 + -13.33333333

Combine like terms: 0 + -13.33333333 = -13.33333333
2.333333333r + r2 = -13.33333333

The r term is 2.333333333r.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333r + 1.361111112 + r2 = -13.33333333 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333r + r2 = -13.33333333 + 1.361111112

Combine like terms: -13.33333333 + 1.361111112 = -11.972222218
1.361111112 + 2.333333333r + r2 = -11.972222218

Factor a perfect square on the left side:
(r + 1.166666667)(r + 1.166666667) = -11.972222218

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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