Answer
Makes sense.
An equation that is quadratic in form is one that can be expressed as a quadratic equation using an $ appropriate$ $substitution $. For instance, to solve for $x$ in the equation, $x^4 - 8x^2 - 9 = 0$, the equation can be rewritten as: $u^2 - 8u - 9 = 0$ by letting $u=x^2$.
Solving for $u$ will give values of $9$ and $-1$.
However, getting the values of $u$ is not the end of the solution. In quadratic equations, what is asked is to solve for $x$. Hence, it is important to take note of the original substitution, $u = x^2$, 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 is one that can be expressed as a quadratic equation using an $ appropriate$ $substitution $. For instance, to solve for $x$ in the equation, $x^4 - 8x^2 - 9 = 0$, the equation can be rewritten as: $u^2 - 8u - 9 = 0$ by letting $u=x^2$.
Solving for $u$ will give values of $9$ and $-1$.
However, getting the values of $u$ is not the end of the solution. In quadratic equations, what is asked is to solve for $x$. Hence, it is important to take note of the original substitution, $u = x^2$, to solve for $x$.
Thus,
$x^2 = 9$
$x = ±3$
$x^2 = -1$
$x=±i$
