x=4x^2-32x+69

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Solution for x=4x^2-32x+69 equation: 


Simplifying
x = 4x2 + -32x + 69

Reorder the terms:
x = 69 + -32x + 4x2

Solving
x = 69 + -32x + 4x2

Solving for variable 'x'.

Reorder the terms:
-69 + x + 32x + -4x2 = 69 + -32x + 4x2 + -69 + 32x + -4x2

Combine like terms: x + 32x = 33x
-69 + 33x + -4x2 = 69 + -32x + 4x2 + -69 + 32x + -4x2

Reorder the terms:
-69 + 33x + -4x2 = 69 + -69 + -32x + 32x + 4x2 + -4x2

Combine like terms: 69 + -69 = 0
-69 + 33x + -4x2 = 0 + -32x + 32x + 4x2 + -4x2
-69 + 33x + -4x2 = -32x + 32x + 4x2 + -4x2

Combine like terms: -32x + 32x = 0
-69 + 33x + -4x2 = 0 + 4x2 + -4x2
-69 + 33x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-69 + 33x + -4x2 = 0

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

Divide each side by '-4'.
17.25 + -8.25x + x2 = 0

Move the constant term to the right:

Add '-17.25' to each side of the equation.
17.25 + -8.25x + -17.25 + x2 = 0 + -17.25

Reorder the terms:
17.25 + -17.25 + -8.25x + x2 = 0 + -17.25

Combine like terms: 17.25 + -17.25 = 0.00
0.00 + -8.25x + x2 = 0 + -17.25
-8.25x + x2 = 0 + -17.25

Combine like terms: 0 + -17.25 = -17.25
-8.25x + x2 = -17.25

The x term is -8.25x.  Take half its coefficient (-4.125).
Square it (17.015625) and add it to both sides.

Add '17.015625' to each side of the equation.
-8.25x + 17.015625 + x2 = -17.25 + 17.015625

Reorder the terms:
17.015625 + -8.25x + x2 = -17.25 + 17.015625

Combine like terms: -17.25 + 17.015625 = -0.234375
17.015625 + -8.25x + x2 = -0.234375

Factor a perfect square on the left side:
(x + -4.125)(x + -4.125) = -0.234375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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