9+x*x=25+(10-x)(10-x)

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Solution for 9+x*x=25+(10-x)(10-x) equation: 


Simplifying
9 + x * x = 25 + (10 + -1x)(10 + -1x)

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

Multiply (10 + -1x) * (10 + -1x)
9 + x2 = 25 + (10(10 + -1x) + -1x * (10 + -1x))
9 + x2 = 25 + ((10 * 10 + -1x * 10) + -1x * (10 + -1x))
9 + x2 = 25 + ((100 + -10x) + -1x * (10 + -1x))
9 + x2 = 25 + (100 + -10x + (10 * -1x + -1x * -1x))
9 + x2 = 25 + (100 + -10x + (-10x + 1x2))

Combine like terms: -10x + -10x = -20x
9 + x2 = 25 + (100 + -20x + 1x2)

Combine like terms: 25 + 100 = 125
9 + x2 = 125 + -20x + 1x2

Solving
9 + x2 = 125 + -20x + 1x2

Solving for variable 'x'.

Reorder the terms:
9 + -125 + 20x + x2 + -1x2 = 125 + -20x + 1x2 + -125 + 20x + -1x2

Combine like terms: 9 + -125 = -116
-116 + 20x + x2 + -1x2 = 125 + -20x + 1x2 + -125 + 20x + -1x2

Combine like terms: x2 + -1x2 = 0
-116 + 20x + 0 = 125 + -20x + 1x2 + -125 + 20x + -1x2
-116 + 20x = 125 + -20x + 1x2 + -125 + 20x + -1x2

Reorder the terms:
-116 + 20x = 125 + -125 + -20x + 20x + 1x2 + -1x2

Combine like terms: 125 + -125 = 0
-116 + 20x = 0 + -20x + 20x + 1x2 + -1x2
-116 + 20x = -20x + 20x + 1x2 + -1x2

Combine like terms: -20x + 20x = 0
-116 + 20x = 0 + 1x2 + -1x2
-116 + 20x = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-116 + 20x = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-29 + 5x) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-29 + 5x)' equal to zero and attempt to solve:

Simplifying
-29 + 5x = 0

Solving
-29 + 5x = 0

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

Add '29' to each side of the equation.
-29 + 29 + 5x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 5x = 0 + 29
5x = 0 + 29

Combine like terms: 0 + 29 = 29
5x = 29

Divide each side by '5'.
x = 5.8

Simplifying
x = 5.8
Solution
x = {5.8}

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