10x^2-46x+65=0

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Solution for 10x^2-46x+65=0 equation:


Simplifying
10x2 + -46x + 65 = 0

Reorder the terms:
65 + -46x + 10x2 = 0

Solving
65 + -46x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
6.5 + -4.6x + x2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + -4.6x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + -4.6x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + -4.6x + x2 = 0 + -6.5
-4.6x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
-4.6x + x2 = -6.5

The x term is -4.6x.  Take half its coefficient (-2.3).
Square it (5.29) and add it to both sides.

Add '5.29' to each side of the equation.
-4.6x + 5.29 + x2 = -6.5 + 5.29

Reorder the terms:
5.29 + -4.6x + x2 = -6.5 + 5.29

Combine like terms: -6.5 + 5.29 = -1.21
5.29 + -4.6x + x2 = -1.21

Factor a perfect square on the left side:
(x + -2.3)(x + -2.3) = -1.21

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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