a^2+4a=-45

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Solution for a^2+4a=-45 equation:


Simplifying
a2 + 4a = -45

Reorder the terms:
4a + a2 = -45

Solving
4a + a2 = -45

Solving for variable 'a'.

Reorder the terms:
45 + 4a + a2 = -45 + 45

Combine like terms: -45 + 45 = 0
45 + 4a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + 4a + -45 + a2 = 0 + -45

Reorder the terms:
45 + -45 + 4a + a2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + 4a + a2 = 0 + -45
4a + a2 = 0 + -45

Combine like terms: 0 + -45 = -45
4a + a2 = -45

The a term is 4a.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4a + 4 + a2 = -45 + 4

Reorder the terms:
4 + 4a + a2 = -45 + 4

Combine like terms: -45 + 4 = -41
4 + 4a + a2 = -41

Factor a perfect square on the left side:
(a + 2)(a + 2) = -41

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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