4x^2-20x+53=0

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Solution for 4x^2-20x+53=0 equation:


Simplifying
4x2 + -20x + 53 = 0

Reorder the terms:
53 + -20x + 4x2 = 0

Solving
53 + -20x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
13.25 + -5x + x2 = 0

Move the constant term to the right:

Add '-13.25' to each side of the equation.
13.25 + -5x + -13.25 + x2 = 0 + -13.25

Reorder the terms:
13.25 + -13.25 + -5x + x2 = 0 + -13.25

Combine like terms: 13.25 + -13.25 = 0.00
0.00 + -5x + x2 = 0 + -13.25
-5x + x2 = 0 + -13.25

Combine like terms: 0 + -13.25 = -13.25
-5x + x2 = -13.25

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -13.25 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -13.25 + 6.25

Combine like terms: -13.25 + 6.25 = -7
6.25 + -5x + x2 = -7

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = -7

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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