10r^2+5=-9r

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Solution for 10r^2+5=-9r equation:


Simplifying
10r2 + 5 = -9r

Reorder the terms:
5 + 10r2 = -9r

Solving
5 + 10r2 = -9r

Solving for variable 'r'.

Reorder the terms:
5 + 9r + 10r2 = -9r + 9r

Combine like terms: -9r + 9r = 0
5 + 9r + 10r2 = 0

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

Divide each side by '10'.
0.5 + 0.9r + r2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.9r + -0.5 + r2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.9r + r2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.9r + r2 = 0 + -0.5
0.9r + r2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.9r + r2 = -0.5

The r term is 0.9r.  Take half its coefficient (0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
0.9r + 0.2025 + r2 = -0.5 + 0.2025

Reorder the terms:
0.2025 + 0.9r + r2 = -0.5 + 0.2025

Combine like terms: -0.5 + 0.2025 = -0.2975
0.2025 + 0.9r + r2 = -0.2975

Factor a perfect square on the left side:
(r + 0.45)(r + 0.45) = -0.2975

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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