What is a solution to (x-3)(x+9)=-27

-6

0

Step-by-step explanation:

By observation we can see one solution is x=0 since this will give us

(0-3)(0+9)=(-3)(9)=-27 which is the result on the right hand side.

Now this is a quadratic equation so it should have another solution. This one doesn't seem as obvious to me.

The goal normally is to get 0 on side and factor if possible or use quadratic formula.  There is also completing the square.

So I'm going to multiply (x-3)(x+9) using foil.

First: x(x)=x^2

Outer: x(9)=9x

Inner: -3(x)=-3x

Last: -3(9)=-27

Combine like terms:

x^2+6x-27

So the equation is:

x^2+6x-27=-27

Add 27 on both sides:

x^2+6x+0=0

x^2+6x=0

Factor x out:

x(x+6)=0

In order for these equation to be true one of the left hand factors need to be 0.

Let's find when x is 0, well that is when x=0.

Let's find when x+6 is 0.

x+6=0 can be solved by subtracting 6 on both sides:

x=-6

The solutions are -6 and 0.

We already checked x=0.

Let's check x=-6:

Plugging in -6 where x is in the given equation:

(-6-3)(-6+9)

(-9)(3)

-27 which is the same as right hand side.

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step-by-step explanation:

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500