-2x(4x+1)=21

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Solution for -2x(4x+1)=21 equation: 


Simplifying
-2x(4x + 1) = 21

Reorder the terms:
-2x(1 + 4x) = 21
(1 * -2x + 4x * -2x) = 21
(-2x + -8x2) = 21

Solving
-2x + -8x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + -2x + -8x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -2x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 2x + 8x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(21 + 2x + 8x2)' equal to zero and attempt to solve:

Simplifying
21 + 2x + 8x2 = 0

Solving
21 + 2x + 8x2 = 0

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

Divide each side by '8'.
2.625 + 0.25x + x2 = 0

Move the constant term to the right:

Add '-2.625' to each side of the equation.
2.625 + 0.25x + -2.625 + x2 = 0 + -2.625

Reorder the terms:
2.625 + -2.625 + 0.25x + x2 = 0 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + 0.25x + x2 = 0 + -2.625
0.25x + x2 = 0 + -2.625

Combine like terms: 0 + -2.625 = -2.625
0.25x + x2 = -2.625

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = -2.625 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = -2.625 + 0.015625

Combine like terms: -2.625 + 0.015625 = -2.609375
0.015625 + 0.25x + x2 = -2.609375

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = -2.609375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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