x(5-x)=4(x+1)

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Solution for x(5-x)=4(x+1) equation:


Simplifying
x(5 + -1x) = 4(x + 1)
(5 * x + -1x * x) = 4(x + 1)
(5x + -1x2) = 4(x + 1)

Reorder the terms:
5x + -1x2 = 4(1 + x)
5x + -1x2 = (1 * 4 + x * 4)
5x + -1x2 = (4 + 4x)

Solving
5x + -1x2 = 4 + 4x

Solving for variable 'x'.

Reorder the terms:
-4 + 5x + -4x + -1x2 = 4 + 4x + -4 + -4x

Combine like terms: 5x + -4x = 1x
-4 + 1x + -1x2 = 4 + 4x + -4 + -4x

Reorder the terms:
-4 + 1x + -1x2 = 4 + -4 + 4x + -4x

Combine like terms: 4 + -4 = 0
-4 + 1x + -1x2 = 0 + 4x + -4x
-4 + 1x + -1x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-4 + 1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
4 + -1x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -1x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -1x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x + x2 = 0 + -4
-1x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-1x + x2 = -4

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -4 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -4 + 0.25

Combine like terms: -4 + 0.25 = -3.75
0.25 + -1x + x2 = -3.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -3.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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