Question

1. Solve the equation 4x^2 -28x=0. Check your solution(s) and state the final solution set.
Show all your work.

Answer 1

you may have to use the quadratic formula but there's a way out of this

Answer 2

You could factor out 4x like this

\[4x(x-7) = 0 \]

Answer 3

and then solve for x, by dividing both sides by 4x

\[(x-7) = \frac{ 0 }{ 4x }\]

this will give you

\[(x-7) = 0 \]

which would then give you x = 7 and x = 0

usually the highest power in gives you a hint at how many solutions here it's

x^2 or x to the second power, so we know that there will be two solutions.


so x = 7 and x = 0

let's plug these back into our original equation

4x(x-7) = 0

x = 0

4(0)(0-7) = 0*7 = 0

and

x = 7

4(7)(7-7)

28(0) = 0

so sometimes you don't always have to use the quadratic formula to find out your solutions that's if you can factor and we-write your quadratic expression.

Answer 4

@phebzluvsyu

\[4x ^{2}-28x \]

notice how these two expressions are the same.

\[4x(x-7)\]

Answer 5

I could show you the other way, the LONG way of doing this and it involves the quadratic formula

Answer 6

Quadratic functions are written in this form: \[ax ^{2}+bx+c \]


and this is the quadratic formula.

\[-b \pm \sqrt{ b ^{2}-4ac}/2a \]

Answer 7

we have

\[4x ^{2}-28x = 0 \]

we compare this to

\[ax ^{2}+bx+c\]

so a = 4 b = 0 and c = -28

Answer 8

we then plug this into the formula here are our solutions

\[\frac{ \sqrt{ (28)^{2}-4(4)(0)} }{ 2(4) }\]

\[\frac{ 28-28 }{ 8 } = 0\]

\[\frac{ 28*2=56 }{ 8 } = 7 \]

@phebzluvsyu