4x^2-4x-1=16

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Solution for 4x^2-4x-1=16 equation:


Simplifying
4x2 + -4x + -1 = 16

Reorder the terms:
-1 + -4x + 4x2 = 16

Solving
-1 + -4x + 4x2 = 16

Solving for variable 'x'.

Reorder the terms:
-1 + -16 + -4x + 4x2 = 16 + -16

Combine like terms: -1 + -16 = -17
-17 + -4x + 4x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-17 + -4x + 4x2 = 0

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

Divide each side by '4'.
-4.25 + -1x + x2 = 0

Move the constant term to the right:

Add '4.25' to each side of the equation.
-4.25 + -1x + 4.25 + x2 = 0 + 4.25

Reorder the terms:
-4.25 + 4.25 + -1x + x2 = 0 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + -1x + x2 = 0 + 4.25
-1x + x2 = 0 + 4.25

Combine like terms: 0 + 4.25 = 4.25
-1x + x2 = 4.25

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 4.25 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 4.25 + 0.25

Combine like terms: 4.25 + 0.25 = 4.5
0.25 + -1x + x2 = 4.5

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(x + -0.5) equal to 2.121320344 and -2.121320344.

Subproblem 1

x + -0.5 = 2.121320344 Simplifying x + -0.5 = 2.121320344 Reorder the terms: -0.5 + x = 2.121320344 Solving -0.5 + x = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.121320344 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.121320344 + 0.5 x = 2.121320344 + 0.5 Combine like terms: 2.121320344 + 0.5 = 2.621320344 x = 2.621320344 Simplifying x = 2.621320344

Subproblem 2

x + -0.5 = -2.121320344 Simplifying x + -0.5 = -2.121320344 Reorder the terms: -0.5 + x = -2.121320344 Solving -0.5 + x = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.121320344 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.121320344 + 0.5 x = -2.121320344 + 0.5 Combine like terms: -2.121320344 + 0.5 = -1.621320344 x = -1.621320344 Simplifying x = -1.621320344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.621320344, -1.621320344}

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