How do you solve $n^2=3n-18$ ?

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Answer 1 · 2018-03-27T12:30:39

See a solution process below:

First, transform the equation into standard quadratic form:

$n^2 - color(red)(3n) + color(blue)(18) = 3n - color(red)(3n) - 18 + color(blue)(18)$

$n^2 - 3n + 18 = 0 - 0$

$n^2 - 3n + 18 = 0$

We can now use the quadratic equation to solve this problem:

For $color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0$ , the values of $x$ which are the solutions to the equation are given by:

$x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))$

Substituting:

$color(red)(1)$ for $color(red)(a)$

$color(blue)(-3)$ for $color(blue)(b)$

$color(green)(18)$ for $color(green)(c)$ gives:

$x = (-color(blue)(-3) +- sqrt(color(blue)((-3))^2 - (4 * color(red)(1) * color(green)(18))))/(2 * color(red)(1))$

$x = (3 +- sqrt(9 - 72))/2$

$x = (3 +- sqrt(-63))/2$

How do you solve n^2=3n-18n^2=3n-18?