When the square of a certain number is decreased by 6 times the number, the result is -9. What is the number?

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Answer 1 · 2016-10-12T16:25:36

The number is $3$ .

$1.$ Set up an equation

$x^2-6x=-9$

$2.$ Set the equation equal to $0$

$x^2-6x=-9$
$x^2-6x+9=0$ $larr$ This is a quadratic equation!

$3.$ Solve for the unknown

Personally, I prefer the quadratic formula over factorising, so...
Plug in and simplify!

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

$x=(6+-sqrt(-6^2– 4xx1xx9))/(2xx1)$

$x=(6+-sqrt(36 – 36))/(2)$

$x=(6+-sqrt(0))/(2)$

$x=6/2$

$x=3$