4x^2-23x+53=5x-8

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Solution for 4x^2-23x+53=5x-8 equation: 


Simplifying
4x2 + -23x + 53 = 5x + -8

Reorder the terms:
53 + -23x + 4x2 = 5x + -8

Reorder the terms:
53 + -23x + 4x2 = -8 + 5x

Solving
53 + -23x + 4x2 = -8 + 5x

Solving for variable 'x'.

Reorder the terms:
53 + 8 + -23x + -5x + 4x2 = -8 + 5x + 8 + -5x

Combine like terms: 53 + 8 = 61
61 + -23x + -5x + 4x2 = -8 + 5x + 8 + -5x

Combine like terms: -23x + -5x = -28x
61 + -28x + 4x2 = -8 + 5x + 8 + -5x

Reorder the terms:
61 + -28x + 4x2 = -8 + 8 + 5x + -5x

Combine like terms: -8 + 8 = 0
61 + -28x + 4x2 = 0 + 5x + -5x
61 + -28x + 4x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
61 + -28x + 4x2 = 0

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

Divide each side by '4'.
15.25 + -7x + x2 = 0

Move the constant term to the right:

Add '-15.25' to each side of the equation.
15.25 + -7x + -15.25 + x2 = 0 + -15.25

Reorder the terms:
15.25 + -15.25 + -7x + x2 = 0 + -15.25

Combine like terms: 15.25 + -15.25 = 0.00
0.00 + -7x + x2 = 0 + -15.25
-7x + x2 = 0 + -15.25

Combine like terms: 0 + -15.25 = -15.25
-7x + x2 = -15.25

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -15.25 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -15.25 + 12.25

Combine like terms: -15.25 + 12.25 = -3
12.25 + -7x + x2 = -3

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = -3

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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