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Worked example: quadratic formula (example 2)

Sal solves the equation -x^2+8x=1 by first bringing it to standard form and then using the quadratic formula. Created by Sal Khan and Monterey Institute for Technology and Education.

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• At , why can't you just simplify the square root of 64-4 into 8-2. Why does that change your answer so much?
• You cannot separate square roots into parts if they have addition/subtraction between terms inside.
• Does the equation HAVE to equal zero?
• In the quadratic form, ax^2+bx+c=0, and cubic equation, ax^3+bx^2+cx+d=0. And, it depends what formula that you need to use.
• How would I find for x in this equation (x-6)(x+9)=0. I mean what is the formula to find this type of particular equation.
(1 vote)
• Take each thing in the parenthesis and set it equal to 0. Then solve for x in each.

x - 6 = 0
x = 6

x + 9 = 0
x = -9

So x equals -9 or 6.
• This may seem like a stupid question, -50=10t-5t^2 .... I'm stuck
• In this example, you can start by trying to find if there is some common divisor of all the elements of your equation, or other way to get t^2 without the 5.
• Why do we say x is equal to something or/ and x is equal to something, but shouldn't it just be and because, we need both values of x in order to draw a parabola, which is a quadratic?
• Think of it this way: Can anything assume two values at the same time? This is not possible, as far as I know. By saying `x` is equal to this `and` that, you are essentially saying that `x` can equal two things at once, which is not the case. So, I always use `or`. But yes, you do need both x values to draw a parabola.
• Does it have to be -8+2√15/-2 and -8-2√15/-2? or can it be -8+60/-2 and -8-60/-2? and Why?
• At , could've I just put ± instead of ∓? If I did, would've I gotten it wrong? When should I use which one?
• Sal noted that it is really the same thing, but the correct symbol is ±, so you would be correct in doing that. Sal uses what it would actually do to make a point.
• At why does Sal cancel out the -1 cancel out as. When they are multiplied together that will give +1 and then we have to add that to the equation. Please help
• I think you are saying the same thing as Sal is, when he says they "cancel out" he is implying they equal to one, but multiplying by 1 does not do anything for you, so you just get -4. So he cancels both the two negatives and multiplying by 1 in one step, you do not add 1 to the equation, you do -4(1).
The way I try to teach my students is to determine the sign, then do the math, so 3 negative signs gives a negative answer and 4*1*1 =4, so you get -4 which is the same.
• Sometimes Sal refers to the square root symbol as the square root sign or the radical, and I'm wondering which word is better for it.

Also, why doesn't Sal divide √15 by that -2?
• 1) The symbol √ is called a radical. If you are working with square roots saying it is a square root is more precise than saying radical. The reason is that there are multiple types of radicals: square roots, cube roots, 4th roots, etc.

2) When we reduce fractions, we divide out commone factors. In Sal's fraction, the numberator has 2 factors: 2 and √15. Once the 2 divided out with the -2 in the denominator, the denomiantor becomes 1. So, there is no additional factor to divide with the √15. Even if you had √15/2, there is no common factor to cancel out.

Hope this helps.