2x-3=4x^2-5x+1

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Solution for 2x-3=4x^2-5x+1 equation:


Simplifying
2x + -3 = 4x2 + -5x + 1

Reorder the terms:
-3 + 2x = 4x2 + -5x + 1

Reorder the terms:
-3 + 2x = 1 + -5x + 4x2

Solving
-3 + 2x = 1 + -5x + 4x2

Solving for variable 'x'.

Reorder the terms:
-3 + -1 + 2x + 5x + -4x2 = 1 + -5x + 4x2 + -1 + 5x + -4x2

Combine like terms: -3 + -1 = -4
-4 + 2x + 5x + -4x2 = 1 + -5x + 4x2 + -1 + 5x + -4x2

Combine like terms: 2x + 5x = 7x
-4 + 7x + -4x2 = 1 + -5x + 4x2 + -1 + 5x + -4x2

Reorder the terms:
-4 + 7x + -4x2 = 1 + -1 + -5x + 5x + 4x2 + -4x2

Combine like terms: 1 + -1 = 0
-4 + 7x + -4x2 = 0 + -5x + 5x + 4x2 + -4x2
-4 + 7x + -4x2 = -5x + 5x + 4x2 + -4x2

Combine like terms: -5x + 5x = 0
-4 + 7x + -4x2 = 0 + 4x2 + -4x2
-4 + 7x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-4 + 7x + -4x2 = 0

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

Divide each side by '-4'.
1 + -1.75x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1.75x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -1.75x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1.75x + x2 = 0 + -1
-1.75x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1.75x + x2 = -1

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = -1 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = -1 + 0.765625

Combine like terms: -1 + 0.765625 = -0.234375
0.765625 + -1.75x + x2 = -0.234375

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = -0.234375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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