Answer
Makes sense.
An equation that is quadratic in form $au^2 + bu + c = 0$ is one that has been expressed as a quadratic equation by letting $u$ be equal to the variable factor that reappears squared.
However, getting the values of $u$ is not the end of the solution because in quadratic equations, what is asked is to solve for $x$.
For example:
Given the equation, $x^4 - 8x^2 - 9 = 0$, it can be rewritten as: $u^2 - 8u - 9 = 0$ by letting $u=x^2$.
Solving for $u$ will give values of $9$ and $-1$.
The original substitution, $u = x^2$ is then used to solve for $x$.
Thus,
$x^2 = 9$
$x = ±3$
$x^2 = -1$
$x=±i$
Work Step by Step
Makes sense.
An equation that is quadratic in form $au^2 + bu + c = 0$ is one that has been expressed as a quadratic equation by letting $u$ be equal to the variable factor that reappears squared.
However, getting the values of $u$ is not the end of the solution because in quadratic equations, what is asked is to solve for $x$.
For example:
Given the equation, $x^4 - 8x^2 - 9 = 0$, it can be rewritten as: $u^2 - 8u - 9 = 0$ by letting $u=x^2$.
Solving for $u$ will give values of $9$ and $-1$.
The original substitution, $u = x^2$ is then used to solve for $x$.
Thus,
$x^2 = 9$
$x = ±3$
$x^2 = -1$
$x=±i$
