(2x^2-9x-4)-(x^2+1)=x^2+14

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Solution for (2x^2-9x-4)-(x^2+1)=x^2+14 equation: 


Simplifying
(2x2 + -9x + -4) + -1(x2 + 1) = x2 + 14

Reorder the terms:
(-4 + -9x + 2x2) + -1(x2 + 1) = x2 + 14

Remove parenthesis around (-4 + -9x + 2x2)
-4 + -9x + 2x2 + -1(x2 + 1) = x2 + 14

Reorder the terms:
-4 + -9x + 2x2 + -1(1 + x2) = x2 + 14
-4 + -9x + 2x2 + (1 * -1 + x2 * -1) = x2 + 14
-4 + -9x + 2x2 + (-1 + -1x2) = x2 + 14

Reorder the terms:
-4 + -1 + -9x + 2x2 + -1x2 = x2 + 14

Combine like terms: -4 + -1 = -5
-5 + -9x + 2x2 + -1x2 = x2 + 14

Combine like terms: 2x2 + -1x2 = 1x2
-5 + -9x + 1x2 = x2 + 14

Reorder the terms:
-5 + -9x + 1x2 = 14 + x2

Solving
-5 + -9x + 1x2 = 14 + x2

Solving for variable 'x'.

Reorder the terms:
-5 + -14 + -9x + 1x2 + -1x2 = 14 + x2 + -14 + -1x2

Combine like terms: -5 + -14 = -19
-19 + -9x + 1x2 + -1x2 = 14 + x2 + -14 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-19 + -9x + 0 = 14 + x2 + -14 + -1x2
-19 + -9x = 14 + x2 + -14 + -1x2

Reorder the terms:
-19 + -9x = 14 + -14 + x2 + -1x2

Combine like terms: 14 + -14 = 0
-19 + -9x = 0 + x2 + -1x2
-19 + -9x = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-19 + -9x = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(19 + 9x) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(19 + 9x)' equal to zero and attempt to solve:

Simplifying
19 + 9x = 0

Solving
19 + 9x = 0

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

Add '-19' to each side of the equation.
19 + -19 + 9x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 9x = 0 + -19
9x = 0 + -19

Combine like terms: 0 + -19 = -19
9x = -19

Divide each side by '9'.
x = -2.111111111

Simplifying
x = -2.111111111
Solution
x = {-2.111111111}

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