x^2+3x=-24

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Solution for x^2+3x=-24 equation: 


Simplifying
x2 + 3x = -24

Reorder the terms:
3x + x2 = -24

Solving
3x + x2 = -24

Solving for variable 'x'.

Reorder the terms:
24 + 3x + x2 = -24 + 24

Combine like terms: -24 + 24 = 0
24 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + 3x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + 3x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + 3x + x2 = 0 + -24
3x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
3x + x2 = -24

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 = -24 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -24 + 2.25

Combine like terms: -24 + 2.25 = -21.75
2.25 + 3x + x2 = -21.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -21.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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