16x=21x+17+4x^2

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Solution for 16x=21x+17+4x^2 equation: 


Simplifying
16x = 21x + 17 + 4x2

Reorder the terms:
16x = 17 + 21x + 4x2

Solving
16x = 17 + 21x + 4x2

Solving for variable 'x'.

Reorder the terms:
-17 + 16x + -21x + -4x2 = 17 + 21x + 4x2 + -17 + -21x + -4x2

Combine like terms: 16x + -21x = -5x
-17 + -5x + -4x2 = 17 + 21x + 4x2 + -17 + -21x + -4x2

Reorder the terms:
-17 + -5x + -4x2 = 17 + -17 + 21x + -21x + 4x2 + -4x2

Combine like terms: 17 + -17 = 0
-17 + -5x + -4x2 = 0 + 21x + -21x + 4x2 + -4x2
-17 + -5x + -4x2 = 21x + -21x + 4x2 + -4x2

Combine like terms: 21x + -21x = 0
-17 + -5x + -4x2 = 0 + 4x2 + -4x2
-17 + -5x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-17 + -5x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(17 + 5x + 4x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(17 + 5x + 4x2)' equal to zero and attempt to solve:

Simplifying
17 + 5x + 4x2 = 0

Solving
17 + 5x + 4x2 = 0

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

Divide each side by '4'.
4.25 + 1.25x + x2 = 0

Move the constant term to the right:

Add '-4.25' to each side of the equation.
4.25 + 1.25x + -4.25 + x2 = 0 + -4.25

Reorder the terms:
4.25 + -4.25 + 1.25x + x2 = 0 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + 1.25x + x2 = 0 + -4.25
1.25x + x2 = 0 + -4.25

Combine like terms: 0 + -4.25 = -4.25
1.25x + x2 = -4.25

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = -4.25 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = -4.25 + 0.390625

Combine like terms: -4.25 + 0.390625 = -3.859375
0.390625 + 1.25x + x2 = -3.859375

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = -3.859375

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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