x^2+16x-30=0 i need help on working this out. not looking for the answer just need help on how to work it. x^2+16x-30=0 i need help on working this out. not looking for the answer just need help on how to work it. @Mathematics

Question

jamesj · Answer

Use the quadratic equation.

If ax^2 + bx + c = 0, then

x = ... what?  

Use that equation.

anonymous · Answer

forgive for i have no clue how to do these equations lol
the only thing i can think of first is to factor it?

anonymous · Answer

would x be 16? thats all i could think of and its in the equation.

anonymous · Answer

$$Quadratic = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$

anonymous · Answer

$$\frac{-16 \pm \sqrt{16^2 - 4(1)(-30)}}{2}$$

anonymous · Answer

but if i factor it how do i get 16 in there?

anonymous · Answer

You can complete the square:
x^2+16x-30=0
x^2+16x      =30
Square half of 16 and add it to both sides.  This creates a perfect square trinomial on the left side.
x^2+16x+64=30+64
(x+8)^2=94                 factor the left side

Square root
$$x+8=\pm \sqrt{94}$$Subtract 8$$x=-8 \pm \sqrt{94}$$

jamesj · Answer

In general there are three ways to solve quadratic equations
1. Factoring
2. Using the quadratic equation
3. Completing the square

The problem for you and this equation is that it is not at all obvious how to factor it.  I.e., it is not at all obvious what are the factors of -30 that add to 16.

Hence you are going to need another method to solve this equation.

It's hard to believe you were given this problem without having being shown the quadratic formula, method 2, as that is usually the method someone would usually go to next.

So I would check your class notes carefully.

Mandolino has just given the solution using method 3, completing the square.  This is also completely legit.

anonymous · Answer

ive been shown examples and read the txt but its just not clicking to me, thats why i have to see step-by step