x^2+(x^2-10x+25)=13

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Solution for x^2+(x^2-10x+25)=13 equation:


Simplifying
x2 + (x2 + -10x + 25) = 13

Reorder the terms:
x2 + (25 + -10x + x2) = 13

Remove parenthesis around (25 + -10x + x2)
x2 + 25 + -10x + x2 = 13

Reorder the terms:
25 + -10x + x2 + x2 = 13

Combine like terms: x2 + x2 = 2x2
25 + -10x + 2x2 = 13

Solving
25 + -10x + 2x2 = 13

Solving for variable 'x'.

Reorder the terms:
25 + -13 + -10x + 2x2 = 13 + -13

Combine like terms: 25 + -13 = 12
12 + -10x + 2x2 = 13 + -13

Combine like terms: 13 + -13 = 0
12 + -10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -5x + x2) = 0

Factor a trinomial.
2((2 + -1x)(3 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {2, 3}

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