(5-x)+10(5+x)=(5+x)(5-x)

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Solution for (5-x)+10(5+x)=(5+x)(5-x) equation: 


Simplifying
(5 + -1x) + 10(5 + x) = (5 + x)(5 + -1x)

Remove parenthesis around (5 + -1x)
5 + -1x + 10(5 + x) = (5 + x)(5 + -1x)
5 + -1x + (5 * 10 + x * 10) = (5 + x)(5 + -1x)
5 + -1x + (50 + 10x) = (5 + x)(5 + -1x)

Reorder the terms:
5 + 50 + -1x + 10x = (5 + x)(5 + -1x)

Combine like terms: 5 + 50 = 55
55 + -1x + 10x = (5 + x)(5 + -1x)

Combine like terms: -1x + 10x = 9x
55 + 9x = (5 + x)(5 + -1x)

Multiply (5 + x) * (5 + -1x)
55 + 9x = (5(5 + -1x) + x(5 + -1x))
55 + 9x = ((5 * 5 + -1x * 5) + x(5 + -1x))
55 + 9x = ((25 + -5x) + x(5 + -1x))
55 + 9x = (25 + -5x + (5 * x + -1x * x))
55 + 9x = (25 + -5x + (5x + -1x2))

Combine like terms: -5x + 5x = 0
55 + 9x = (25 + 0 + -1x2)
55 + 9x = (25 + -1x2)

Solving
55 + 9x = 25 + -1x2

Solving for variable 'x'.

Reorder the terms:
55 + -25 + 9x + x2 = 25 + -1x2 + -25 + x2

Combine like terms: 55 + -25 = 30
30 + 9x + x2 = 25 + -1x2 + -25 + x2

Reorder the terms:
30 + 9x + x2 = 25 + -25 + -1x2 + x2

Combine like terms: 25 + -25 = 0
30 + 9x + x2 = 0 + -1x2 + x2
30 + 9x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
30 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + 9x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + 9x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + 9x + x2 = 0 + -30
9x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
9x + x2 = -30

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -30 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -30 + 20.25

Combine like terms: -30 + 20.25 = -9.75
20.25 + 9x + x2 = -9.75

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = -9.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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