(X+4)(X+6)=5X+3

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Solution for (X+4)(X+6)=5X+3 equation: 


Simplifying
(X + 4)(X + 6) = 5X + 3

Reorder the terms:
(4 + X)(X + 6) = 5X + 3

Reorder the terms:
(4 + X)(6 + X) = 5X + 3

Multiply (4 + X) * (6 + X)
(4(6 + X) + X(6 + X)) = 5X + 3
((6 * 4 + X * 4) + X(6 + X)) = 5X + 3
((24 + 4X) + X(6 + X)) = 5X + 3
(24 + 4X + (6 * X + X * X)) = 5X + 3
(24 + 4X + (6X + X2)) = 5X + 3

Combine like terms: 4X + 6X = 10X
(24 + 10X + X2) = 5X + 3

Reorder the terms:
24 + 10X + X2 = 3 + 5X

Solving
24 + 10X + X2 = 3 + 5X

Solving for variable 'X'.

Reorder the terms:
24 + -3 + 10X + -5X + X2 = 3 + 5X + -3 + -5X

Combine like terms: 24 + -3 = 21
21 + 10X + -5X + X2 = 3 + 5X + -3 + -5X

Combine like terms: 10X + -5X = 5X
21 + 5X + X2 = 3 + 5X + -3 + -5X

Reorder the terms:
21 + 5X + X2 = 3 + -3 + 5X + -5X

Combine like terms: 3 + -3 = 0
21 + 5X + X2 = 0 + 5X + -5X
21 + 5X + X2 = 5X + -5X

Combine like terms: 5X + -5X = 0
21 + 5X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + 5X + -21 + X2 = 0 + -21

Reorder the terms:
21 + -21 + 5X + X2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 5X + X2 = 0 + -21
5X + X2 = 0 + -21

Combine like terms: 0 + -21 = -21
5X + X2 = -21

The X term is 5X.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5X + 6.25 + X2 = -21 + 6.25

Reorder the terms:
6.25 + 5X + X2 = -21 + 6.25

Combine like terms: -21 + 6.25 = -14.75
6.25 + 5X + X2 = -14.75

Factor a perfect square on the left side:
(X + 2.5)(X + 2.5) = -14.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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