(x*x)+(4*4)=((5-x)(5-x))+(3*3)

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Solution for (x*x)+(4*4)=((5-x)(5-x))+(3*3) equation: 


Simplifying
(x * x) + (4 * 4) = ((5 + -1x)(5 + -1x)) + (3 * 3)

Multiply x * x
(x2) + (4 * 4) = ((5 + -1x)(5 + -1x)) + (3 * 3)
x2 + (4 * 4) = ((5 + -1x)(5 + -1x)) + (3 * 3)

Multiply 4 * 4
x2 + (16) = ((5 + -1x)(5 + -1x)) + (3 * 3)
x2 + 16 = ((5 + -1x)(5 + -1x)) + (3 * 3)

Reorder the terms:
16 + x2 = ((5 + -1x)(5 + -1x)) + (3 * 3)

Multiply (5 + -1x) * (5 + -1x)
16 + x2 = ((5(5 + -1x) + -1x * (5 + -1x))) + (3 * 3)
16 + x2 = (((5 * 5 + -1x * 5) + -1x * (5 + -1x))) + (3 * 3)
16 + x2 = (((25 + -5x) + -1x * (5 + -1x))) + (3 * 3)
16 + x2 = ((25 + -5x + (5 * -1x + -1x * -1x))) + (3 * 3)
16 + x2 = ((25 + -5x + (-5x + 1x2))) + (3 * 3)

Combine like terms: -5x + -5x = -10x
16 + x2 = ((25 + -10x + 1x2)) + (3 * 3)
16 + x2 = (25 + -10x + 1x2) + (3 * 3)

Remove parenthesis around (25 + -10x + 1x2)
16 + x2 = 25 + -10x + 1x2 + (3 * 3)

Multiply 3 * 3
16 + x2 = 25 + -10x + 1x2 + (9)
16 + x2 = 25 + -10x + 1x2 + 9

Reorder the terms:
16 + x2 = 25 + 9 + -10x + 1x2

Combine like terms: 25 + 9 = 34
16 + x2 = 34 + -10x + 1x2

Solving
16 + x2 = 34 + -10x + 1x2

Solving for variable 'x'.

Reorder the terms:
16 + -34 + 10x + x2 + -1x2 = 34 + -10x + 1x2 + -34 + 10x + -1x2

Combine like terms: 16 + -34 = -18
-18 + 10x + x2 + -1x2 = 34 + -10x + 1x2 + -34 + 10x + -1x2

Combine like terms: x2 + -1x2 = 0
-18 + 10x + 0 = 34 + -10x + 1x2 + -34 + 10x + -1x2
-18 + 10x = 34 + -10x + 1x2 + -34 + 10x + -1x2

Reorder the terms:
-18 + 10x = 34 + -34 + -10x + 10x + 1x2 + -1x2

Combine like terms: 34 + -34 = 0
-18 + 10x = 0 + -10x + 10x + 1x2 + -1x2
-18 + 10x = -10x + 10x + 1x2 + -1x2

Combine like terms: -10x + 10x = 0
-18 + 10x = 0 + 1x2 + -1x2
-18 + 10x = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-18 + 10x = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 5x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + 5x)' equal to zero and attempt to solve:

Simplifying
-9 + 5x = 0

Solving
-9 + 5x = 0

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

Add '9' to each side of the equation.
-9 + 9 + 5x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 5x = 0 + 9
5x = 0 + 9

Combine like terms: 0 + 9 = 9
5x = 9

Divide each side by '5'.
x = 1.8

Simplifying
x = 1.8
Solution
x = {1.8}

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