(x+5)(x+5)=(x+4)(x+4)

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


Simplifying
(x + 5)(x + 5) = (x + 4)(x + 4)

Reorder the terms:
(5 + x)(x + 5) = (x + 4)(x + 4)

Reorder the terms:
(5 + x)(5 + x) = (x + 4)(x + 4)

Multiply (5 + x) * (5 + x)
(5(5 + x) + x(5 + x)) = (x + 4)(x + 4)
((5 * 5 + x * 5) + x(5 + x)) = (x + 4)(x + 4)
((25 + 5x) + x(5 + x)) = (x + 4)(x + 4)
(25 + 5x + (5 * x + x * x)) = (x + 4)(x + 4)
(25 + 5x + (5x + x2)) = (x + 4)(x + 4)

Combine like terms: 5x + 5x = 10x
(25 + 10x + x2) = (x + 4)(x + 4)

Reorder the terms:
25 + 10x + x2 = (4 + x)(x + 4)

Reorder the terms:
25 + 10x + x2 = (4 + x)(4 + x)

Multiply (4 + x) * (4 + x)
25 + 10x + x2 = (4(4 + x) + x(4 + x))
25 + 10x + x2 = ((4 * 4 + x * 4) + x(4 + x))
25 + 10x + x2 = ((16 + 4x) + x(4 + x))
25 + 10x + x2 = (16 + 4x + (4 * x + x * x))
25 + 10x + x2 = (16 + 4x + (4x + x2))

Combine like terms: 4x + 4x = 8x
25 + 10x + x2 = (16 + 8x + x2)

Add '-1x2' to each side of the equation.
25 + 10x + x2 + -1x2 = 16 + 8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
25 + 10x + 0 = 16 + 8x + x2 + -1x2
25 + 10x = 16 + 8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
25 + 10x = 16 + 8x + 0
25 + 10x = 16 + 8x

Solving
25 + 10x = 16 + 8x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-8x' to each side of the equation.
25 + 10x + -8x = 16 + 8x + -8x

Combine like terms: 10x + -8x = 2x
25 + 2x = 16 + 8x + -8x

Combine like terms: 8x + -8x = 0
25 + 2x = 16 + 0
25 + 2x = 16

Add '-25' to each side of the equation.
25 + -25 + 2x = 16 + -25

Combine like terms: 25 + -25 = 0
0 + 2x = 16 + -25
2x = 16 + -25

Combine like terms: 16 + -25 = -9
2x = -9

Divide each side by '2'.
x = -4.5

Simplifying
x = -4.5

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