7a-5a(a-3)=27

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Solution for 7a-5a(a-3)=27 equation:


Simplifying
7a + -5a(a + -3) = 27

Reorder the terms:
7a + -5a(-3 + a) = 27
7a + (-3 * -5a + a * -5a) = 27
7a + (15a + -5a2) = 27

Combine like terms: 7a + 15a = 22a
22a + -5a2 = 27

Solving
22a + -5a2 = 27

Solving for variable 'a'.

Reorder the terms:
-27 + 22a + -5a2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + 22a + -5a2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
5.4 + -4.4a + a2 = 0

Move the constant term to the right:

Add '-5.4' to each side of the equation.
5.4 + -4.4a + -5.4 + a2 = 0 + -5.4

Reorder the terms:
5.4 + -5.4 + -4.4a + a2 = 0 + -5.4

Combine like terms: 5.4 + -5.4 = 0.0
0.0 + -4.4a + a2 = 0 + -5.4
-4.4a + a2 = 0 + -5.4

Combine like terms: 0 + -5.4 = -5.4
-4.4a + a2 = -5.4

The a term is -4.4a.  Take half its coefficient (-2.2).
Square it (4.84) and add it to both sides.

Add '4.84' to each side of the equation.
-4.4a + 4.84 + a2 = -5.4 + 4.84

Reorder the terms:
4.84 + -4.4a + a2 = -5.4 + 4.84

Combine like terms: -5.4 + 4.84 = -0.56
4.84 + -4.4a + a2 = -0.56

Factor a perfect square on the left side:
(a + -2.2)(a + -2.2) = -0.56

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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