Question

Please help! use the quadratic formula to solve the equations
1. 5x^2 + 16x - 84 = 0
2. 3x^2 - 41x = -110
3. 2x^2 - x - 120 = 0

Answer 1

@AccessDenied could you help????

Answer 2

Have you tried using the quadratic formula in each case?
The quadratic formula's statement is as follows:
The solution to the quadratic equation \( \color{red}ax^2 + \color{green}bx + \color{blue}c = 0 \) is given by the formula:
\( x = \dfrac{-\color{green}b \pm \sqrt{\color{green}b^2 - 4\color{red}a\color{blue}c}}{2\color{red}a} \)

So once you have the equation set equal to zero, it just comes down to plugging in those coefficients.

Answer 3

As an example:
5x^2 + 16x - 84 = 0
This is already in the format \(ax^2 + bx + c = 0\). So we use the coefficients: a = 5, b = 16, and c = -84:
\( x = \dfrac{ -\color{green}{16} \pm \sqrt{\color{Green}{16}^2 - 4 (\color{red}5) (\color{blue}{-84})}}{2(\color{red}5)} \)

Answer 4

im still confused

Answer 5

Hmm.. is there a specific part that doesn't make sense?

Answer 6

im not sure hot to solve it

Answer 7

*how

Answer 8

The quadratic formula gives you the solutions to the quadratic equation immediately. You just need to do some simplifications by arithmetic / calculator on the result.

If you had the equation \(x^2 - 2x + 1 = 0 \) which easily factors into (x - 1)(x - 1) = 0 with solution x = 1, the quadratic formula statement is:
\( x = \dfrac{2 \pm \sqrt{(-2)^2 - 4(1)(1)}}{2} = \dfrac{2 \pm 0}{2} = 1 \)
Thus both predict the same solution.

Answer 9

so the answer for the first question would be x = -6 and or x = 14/5????

Answer 10

Looks good to me. :)

Answer 11

2.) is the only trickier one because they do NOT have the equation in the form \(ax^2 + bx + c = 0\). You need to do a small initial step arranging so that one side of the equation is zero before applying the formula.

Answer 12

I have to go to bed could you still explain how to do everything and i could look at it in the morning???

Answer 13

It is the same process as the first problem really.

\( 3x^2 -41 x = -110 \) Just move the -110 to the left-hand side by adding 110 to both sides
\( 3x^2 - 41 x + 110 = 0\) and now use the coefficients a=3, b=-41, and c=110.

The last one is already in correct form.

Answer 14

i will look over this again in the morning if i have any more questions about this i will ask

Answer 15

And if you are ever uncertain about the answers, you can always check by evaluating the equation for x = your solution. Getting 0 = 0 is a successful solution. :)

Anyways, gnight!

Answer 16

thank you

Answer 17

Did you have more questions on this?

Answer 18

not yet