7x-10=8-x^2

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Solution for 7x-10=8-x^2 equation: 


Simplifying
7x + -10 = 8 + -1x2

Reorder the terms:
-10 + 7x = 8 + -1x2

Solving
-10 + 7x = 8 + -1x2

Solving for variable 'x'.

Reorder the terms:
-10 + -8 + 7x + x2 = 8 + -1x2 + -8 + x2

Combine like terms: -10 + -8 = -18
-18 + 7x + x2 = 8 + -1x2 + -8 + x2

Reorder the terms:
-18 + 7x + x2 = 8 + -8 + -1x2 + x2

Combine like terms: 8 + -8 = 0
-18 + 7x + x2 = 0 + -1x2 + x2
-18 + 7x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-18 + 7x + x2 = 0

Factor a trinomial.
(-9 + -1x)(2 + -1x) = 0


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

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

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

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

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
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
Solution
x = {-9, 2}

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