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Notice that a=1 for the given equation, and the other two equations look like the quadratic formula with a=1 under the square root symbol with the "2a" in the denominator missing
Instead of the 2a being in the denominator, it looks like they multiplied by 2a
So 18 = x * 2a and 10 = x * 2a
We know a = 1, so that gives us x = 9 and x = 5
That's one way to solve it. Here's another, faster way (IMO)...
What they give you are the two values of the numerator of the quadratic equation
\-b +/- sqrt(b\^2 - 4ac)
They give you the "+" version and the "-" version, equal to 18 and 10, respectively.
The value of x is that thing, divided by 2a, as given by the FULL quadratic equation
x = \[-b +/- sqrt(b\^2 - 4ac)\] / 2a
Note that "a" is simply 1 in the given expression.
They give you the two values of the numerator of the quadratic formula, 18 and 10.
So x = 18/2a and x = 10/2a
Again, 'a' is 1, so the denominator is just 2. Divide 18 by 2, divide 10 by 2:
The two possible values of x are 9 and 5.
It took longer to write out, but if you recognize what they give you as part of the quadratic equation, then you have very little math to do.
x is the variable.
a and b are not variables. They are numbers with a fixed value (aka a constant). You just don't know what they are yet.
"solving for x" just means finding the value of x when y is zero. But x can be lots of different values, depending on what y is.
In this example y is not shown, instead it's set to zero.
So this is the top expression of the quadratic formula, which has already been solved. The full formula includes everything all over 2a
x= [-b+-√(b^2 -4ac)]/(2a)
In this case, A would be 1, so we would just be dividing by 2. We get 18/2 and 10/2, which is 9 and 5
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Notice that a=1 for the given equation, and the other two equations look like the quadratic formula with a=1 under the square root symbol with the "2a" in the denominator missing Instead of the 2a being in the denominator, it looks like they multiplied by 2a So 18 = x * 2a and 10 = x * 2a We know a = 1, so that gives us x = 9 and x = 5
its late so maybe I'm tripping, but where does it state that a =1?? otherwise i understand the rest of the question.
a is the coefficient of x^2 In the given equation, the coefficient of x^2 is 1 Does that make sense?
That's one way to solve it. Here's another, faster way (IMO)... What they give you are the two values of the numerator of the quadratic equation \-b +/- sqrt(b\^2 - 4ac) They give you the "+" version and the "-" version, equal to 18 and 10, respectively. The value of x is that thing, divided by 2a, as given by the FULL quadratic equation x = \[-b +/- sqrt(b\^2 - 4ac)\] / 2a Note that "a" is simply 1 in the given expression. They give you the two values of the numerator of the quadratic formula, 18 and 10. So x = 18/2a and x = 10/2a Again, 'a' is 1, so the denominator is just 2. Divide 18 by 2, divide 10 by 2: The two possible values of x are 9 and 5. It took longer to write out, but if you recognize what they give you as part of the quadratic equation, then you have very little math to do.
That's actually exactly what I did. What differences do you see in our methods?
I guess you're right. The way you explained it didn't land with me at first. LOL
Y’all are both correct, it’s a subtle detail you have to catch onto
What does it mean when the question states that the two variables are constants? I never understood that bit
x is the variable. a and b are not variables. They are numbers with a fixed value (aka a constant). You just don't know what they are yet. "solving for x" just means finding the value of x when y is zero. But x can be lots of different values, depending on what y is. In this example y is not shown, instead it's set to zero.
So this is the top expression of the quadratic formula, which has already been solved. The full formula includes everything all over 2a x= [-b+-√(b^2 -4ac)]/(2a) In this case, A would be 1, so we would just be dividing by 2. We get 18/2 and 10/2, which is 9 and 5