(2x+1)=4(x^2+x+1)

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


Simplifying
(2x + 1) = 4(x2 + x + 1)

Reorder the terms:
(1 + 2x) = 4(x2 + x + 1)

Remove parenthesis around (1 + 2x)
1 + 2x = 4(x2 + x + 1)

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

Solving
1 + 2x = 4 + 4x + 4x2

Solving for variable 'x'.

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

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

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

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

Combine like terms: 4 + -4 = 0
-3 + -2x + -4x2 = 0 + 4x + -4x + 4x2 + -4x2
-3 + -2x + -4x2 = 4x + -4x + 4x2 + -4x2

Combine like terms: 4x + -4x = 0
-3 + -2x + -4x2 = 0 + 4x2 + -4x2
-3 + -2x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-3 + -2x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 2x + 4x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(3 + 2x + 4x2)' equal to zero and attempt to solve:

Simplifying
3 + 2x + 4x2 = 0

Solving
3 + 2x + 4x2 = 0

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

Divide each side by '4'.
0.75 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 0.5x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 0.5x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 0.5x + x2 = 0 + -0.75
0.5x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
0.5x + x2 = -0.75

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = -0.75 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = -0.75 + 0.0625

Combine like terms: -0.75 + 0.0625 = -0.6875
0.0625 + 0.5x + x2 = -0.6875

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = -0.6875

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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