4x^2+8x+21=1

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Solution for 4x^2+8x+21=1 equation:


Simplifying
4x2 + 8x + 21 = 1

Reorder the terms:
21 + 8x + 4x2 = 1

Solving
21 + 8x + 4x2 = 1

Solving for variable 'x'.

Reorder the terms:
21 + -1 + 8x + 4x2 = 1 + -1

Combine like terms: 21 + -1 = 20
20 + 8x + 4x2 = 1 + -1

Combine like terms: 1 + -1 = 0
20 + 8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + 2x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
5 + 2x + x2 = 0

Solving
5 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 2x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 2x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x + x2 = 0 + -5
2x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
2x + x2 = -5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -5 + 1

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

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

Factor a perfect square on the left side:
(x + 1)(x + 1) = -4

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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