h^2-6h=72 how do you find h?

Question

johnweldon1993 · Answer

We can either factor, or complete the square

anonymous · Answer

the answer should be 12 but I need to work it out and I don't know how to

anonymous · Answer

First set it equal to zero then you can use @johnweldon1993 method or even the quadratic formula

anonymous · Answer

can you add the h^2 and the -6h

johnweldon1993 · Answer

To factor, subtract 72 from both sides

$$\large h^2 - 6h - 72$$

Now find the factors of -72 that also add up to -6

***also, there will be 2 answers***

johnweldon1993 · Answer

So lets see

1 and 72
2 and 36
3 and 24
4 and 18
6 and 12    <--- oh look

We know that 6 and 12 can somehow be combined to add to -6

$$\large (x - 12)(x + 6)$$

This shows us that both 12 and -6 can be answers to our equation

anonymous · Answer

well there is suppose to only be one answer so how do I work it out so I can only get one asnwer

johnweldon1993 · Answer

You cannot, there will always be 2 answers to a quadratic equation, perhaps the teacher may only want 1 answer recorded, however this is technically wrong since there WILL be 2 results

johnweldon1993 · Answer

We can use another method to show that too, completing the square

$$\large h^2 - 6h = 72$$

Take half the coefficient of the 'h' (which is -6) divide it by 2 (so -3) and then square that result (so that will come out to 9)

Now add that to both sides

$$\large h^2 - 6h + 9 = 72 + 9$$

$$\large h^2 - 6h + 9 = 81$$

Turn the left hand side into a perfect square

$$\large (h - 3)^2 = 81$$

take the square root of both sides

$$\large h - 3 = \pm 9$$

This will lead to 2 equations

$\large h - 3 = 9$ and $\large h - 3 = -9$

solving both f those we get

$\large h = 12$ and $\large h = -6$

anonymous · Answer

the area of a triangle is given by the equation h^2-6h=72   where h is the height of the triangle. what is the value of h? there should only be one answer

johnweldon1993 · Answer

So the teacher is justified in asking for only 1 answer, we cannot have a negative area, the item would be in some parallel universe for that to happen,

so 12 would be the answer recorded there

anonymous · Answer

ok so if 12 is the answer how did you get 12