-9x+2=x^2+16

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Solution for -9x+2=x^2+16 equation: 


Simplifying
-9x + 2 = x2 + 16

Reorder the terms:
2 + -9x = x2 + 16

Reorder the terms:
2 + -9x = 16 + x2

Solving
2 + -9x = 16 + x2

Solving for variable 'x'.

Reorder the terms:
2 + -16 + -9x + -1x2 = 16 + x2 + -16 + -1x2

Combine like terms: 2 + -16 = -14
-14 + -9x + -1x2 = 16 + x2 + -16 + -1x2

Reorder the terms:
-14 + -9x + -1x2 = 16 + -16 + x2 + -1x2

Combine like terms: 16 + -16 = 0
-14 + -9x + -1x2 = 0 + x2 + -1x2
-14 + -9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-14 + -9x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 9x + x2) = 0

Factor a trinomial.
-1((7 + x)(2 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {-7, -2}

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