Question

solve the equation 24x^2-17x=0
x=

Answer 1

factor out an x

x(24x - 17) = 0

now you should be able to solve for x

Answer 2

@agent0smith @amistre64 @Jamierox4ev3r @jdoe0001 @pitamar

Answer 3

im lost @campbell_st

Answer 4

well now you have 2 parts that multiply to 0

if either part is zero the whole equation has a value of zero

so you need to solve

x = 0 and 24x - 17 = 0

obviously x = 0 is a solution, but you need to find the other

Answer 5

@campbell_st is the answer 7

Answer 6

Well, I honestly think campbell's solution is good and clear, but it seems you're having troubles, so I'll try to explain

We know that
\[
24x^2 - 17x = 0
\]
You have to remember, that what we're looking for are all the possible values for 'x' so the equation is true. for example, x=1 is wrong because
\[
24 \cdot 1^2 - 17\cdot 1 = 0 \quad \to \quad 24-17 = 0 \quad \to \quad 7 \ne 0
\]
So, to find those solutions we can do as campbell suggested
We can write it a bit differently:
\[
24x^2 - 17x = 0 \quad \to \quad x \cdot (24x - 17) = 0
\]
Now, just like campbell has said, we have 2 parts that multiply to zero.
As you know, in order for the product to be zero, one of the factors has to be zero.
So.. That means... In order for x(24x - 17) to be 0.. either the 'x' has to be 0, or the (24x-17)
So we say
\[
x = 0 \quad \text or \quad (24x-17) = 0
\]
So, x=0 is one solution we get that fits in the equation and we can even check that
\[
27 \cdot 0^2 - 17\cdot 0 = 0 \quad \to \quad 0 = 0
\]
But since (24x-17) = 0 would also give us a right solution, then:
\[
(24x - 17) = 0 \quad// \text{Add 17 to both sides}\\
24x = 17 \quad // \text{ Divide both sides by 24}\\
x = \frac{17}{24}
\]
Ugly, but fits in:
\[
24 \cdot \bigg[ \frac{17}{24} \bigg]^2 - 17 \cdot \frac{17}{24} = 0 \\
\frac{24 \cdot 17^2}{24^2} - \frac{17 \cdot 17}{24} = 0 \\
\frac{17^2}{24} - \frac{17^2}{24} = 0 \\
0 = 0
\]
So:
\[
x = 0 \quad \text{ or } \quad x = \frac{17}{24}
\]