x(x-1)=90

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Solution for x(x-1)=90 equation:


Simplifying
x(x + -1) = 90

Reorder the terms:
x(-1 + x) = 90
(-1 * x + x * x) = 90
(-1x + x2) = 90

Solving
-1x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + -1x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -1x + x2 = 0

Factor a trinomial.
(-9 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10

Solution

x = {-9, 10}

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