How do you solve the equation: $x^2 + 24x + 90 = 0$ ?

Question

1912 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-03T06:35:43

Check the discriminant, then use the quadratic formula to find:

$x = -12 +-3sqrt(6)$ .

That is:

$x = -12-3sqrt(6)$ or $x = -12+3sqrt(6)$

$f(x) = x^2+24x+90$ is of the form

$ax^2+bx+c$ with $a=1$ , $b=24$ and $c=90$ .

This has discriminant $Delta$ given by the formula:

$Delta = b^2-4ac = 24^2-(4xx1xx90) = 576 - 360$

$= 216 = 6^2*6$

Since $Delta$ is positive, but not a perfect square, $f(x) = 0$ has two distinct irrational real solutions, given by the quadratic formula:

$x = (-b+-sqrt(b^2-4ac))/(2a)$

$= (-b+-sqrt(Delta))/(2a)$

$= (-24+-sqrt(216))/2$

$= (-24+-6sqrt(6))/2$

$=-12+-3sqrt(6)$

How do you solve the equation: x^2 + 24x + 90 = 0x^2 + 24x + 90 = 0?