x^2-81=80x

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Solution for x^2-81=80x equation:


Simplifying
x2 + -81 = 80x

Reorder the terms:
-81 + x2 = 80x

Solving
-81 + x2 = 80x

Solving for variable 'x'.

Reorder the terms:
-81 + -80x + x2 = 80x + -80x

Combine like terms: 80x + -80x = 0
-81 + -80x + x2 = 0

Factor a trinomial.
(-1 + -1x)(81 + -1x) = 0

Subproblem 1

Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1

Subproblem 2

Set the factor '(81 + -1x)' equal to zero and attempt to solve: Simplifying 81 + -1x = 0 Solving 81 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-81' to each side of the equation. 81 + -81 + -1x = 0 + -81 Combine like terms: 81 + -81 = 0 0 + -1x = 0 + -81 -1x = 0 + -81 Combine like terms: 0 + -81 = -81 -1x = -81 Divide each side by '-1'. x = 81 Simplifying x = 81

Solution

x = {-1, 81}

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