100x^2+90x+65=0

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Solution for 100x^2+90x+65=0 equation: 


Simplifying
100x2 + 90x + 65 = 0

Reorder the terms:
65 + 90x + 100x2 = 0

Solving
65 + 90x + 100x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(13 + 18x + 20x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(13 + 18x + 20x2)' equal to zero and attempt to solve:

Simplifying
13 + 18x + 20x2 = 0

Solving
13 + 18x + 20x2 = 0

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

Divide each side by '20'.
0.65 + 0.9x + x2 = 0.0

Move the constant term to the right:

Add '-0.65' to each side of the equation.
0.65 + 0.9x + -0.65 + x2 = 0.0 + -0.65

Reorder the terms:
0.65 + -0.65 + 0.9x + x2 = 0.0 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + 0.9x + x2 = 0.0 + -0.65
0.9x + x2 = 0.0 + -0.65

Combine like terms: 0.0 + -0.65 = -0.65
0.9x + x2 = -0.65

The x term is 0.9x.  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.
0.9x + 0.2025 + x2 = -0.65 + 0.2025

Reorder the terms:
0.2025 + 0.9x + x2 = -0.65 + 0.2025

Combine like terms: -0.65 + 0.2025 = -0.4475
0.2025 + 0.9x + x2 = -0.4475

Factor a perfect square on the left side:
(x + 0.45)(x + 0.45) = -0.4475

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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