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.

step- i d k and i d c : )

you: : 0

bye

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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