(100-x)-9x(x-100)=0

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Solution for (100-x)-9x(x-100)=0 equation:


Simplifying
(100 + -1x) + -9x(x + -100) = 0

Remove parenthesis around (100 + -1x)
100 + -1x + -9x(x + -100) = 0

Reorder the terms:
100 + -1x + -9x(-100 + x) = 0
100 + -1x + (-100 * -9x + x * -9x) = 0
100 + -1x + (900x + -9x2) = 0

Combine like terms: -1x + 900x = 899x
100 + 899x + -9x2 = 0

Solving
100 + 899x + -9x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(100 + -1x)(1 + 9x) = 0

Subproblem 1

Set the factor '(100 + -1x)' equal to zero and attempt to solve: Simplifying 100 + -1x = 0 Solving 100 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + -1x = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -1x = 0 + -100 -1x = 0 + -100 Combine like terms: 0 + -100 = -100 -1x = -100 Divide each side by '-1'. x = 100 Simplifying x = 100

Subproblem 2

Set the factor '(1 + 9x)' equal to zero and attempt to solve: Simplifying 1 + 9x = 0 Solving 1 + 9x = 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 + 9x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 9x = 0 + -1 9x = 0 + -1 Combine like terms: 0 + -1 = -1 9x = -1 Divide each side by '9'. x = -0.1111111111 Simplifying x = -0.1111111111

Solution

x = {100, -0.1111111111}

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