0=x^2+3x+54

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Solution for 0=x^2+3x+54 equation:


Simplifying
0 = x2 + 3x + 54

Reorder the terms:
0 = 54 + 3x + x2

Solving
0 = 54 + 3x + x2

Solving for variable 'x'.

Combine like terms: 0 + -54 = -54
-54 + -3x + -1x2 = 54 + 3x + x2 + -54 + -3x + -1x2

Reorder the terms:
-54 + -3x + -1x2 = 54 + -54 + 3x + -3x + x2 + -1x2

Combine like terms: 54 + -54 = 0
-54 + -3x + -1x2 = 0 + 3x + -3x + x2 + -1x2
-54 + -3x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
-54 + -3x + -1x2 = 0 + x2 + -1x2
-54 + -3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-54 + -3x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(54 + 3x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(54 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
54 + 3x + x2 = 0

Solving
54 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-54' to each side of the equation.
54 + 3x + -54 + x2 = 0 + -54

Reorder the terms:
54 + -54 + 3x + x2 = 0 + -54

Combine like terms: 54 + -54 = 0
0 + 3x + x2 = 0 + -54
3x + x2 = 0 + -54

Combine like terms: 0 + -54 = -54
3x + x2 = -54

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -54 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -54 + 2.25

Combine like terms: -54 + 2.25 = -51.75
2.25 + 3x + x2 = -51.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -51.75

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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