34-x^2=x^2-4x+4

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Solution for 34-x^2=x^2-4x+4 equation: 


Simplifying
34 + -1x2 = x2 + -4x + 4

Reorder the terms:
34 + -1x2 = 4 + -4x + x2

Solving
34 + -1x2 = 4 + -4x + x2

Solving for variable 'x'.

Reorder the terms:
34 + -4 + 4x + -1x2 + -1x2 = 4 + -4x + x2 + -4 + 4x + -1x2

Combine like terms: 34 + -4 = 30
30 + 4x + -1x2 + -1x2 = 4 + -4x + x2 + -4 + 4x + -1x2

Combine like terms: -1x2 + -1x2 = -2x2
30 + 4x + -2x2 = 4 + -4x + x2 + -4 + 4x + -1x2

Reorder the terms:
30 + 4x + -2x2 = 4 + -4 + -4x + 4x + x2 + -1x2

Combine like terms: 4 + -4 = 0
30 + 4x + -2x2 = 0 + -4x + 4x + x2 + -1x2
30 + 4x + -2x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
30 + 4x + -2x2 = 0 + x2 + -1x2
30 + 4x + -2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
30 + 4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 2x + -1x2) = 0

Factor a trinomial.
2((5 + -1x)(3 + x)) = 0

Ignore the factor 2.

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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {5, -3}

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