Question

Please Help! Quadratic Formula
One number is 5 more than aother number. Find these numbers if their product is -3.

Answer 1

Let one number be X.

Other number = X - 5

Product = (x)(x-5) = -3
thus x^2 - 5x + 3 = 0
solve for x:

(x-3)(x-2)=0

Answer 2

Let the smaller number be x
The other number is 5 more so it is x + 5
Their product is -3, so
\( x (x + 5) = -3 \)

Answer 3

\(x (x + 5) = -3 \)

\(x^2 + 5x + 3 = 0 \)

This is not factorable, so you need to use the quadratic formula as tye problem states.

Answer 4

^the

Answer 5

Do the quadratic formula again because that's not correct.

Answer 6

\(x = \dfrac{-b \pm \sqrt{ b^2 - 4ac}} {2a} \)

Answer 7

\( x = \dfrac{-5 \pm \sqrt{ 5^2 - 4(1)(3)}} {2(1)} \)

Answer 8

Just substitute all your terms into the equation, can you list me the value of each term A,B, and C ?

Answer 9

Nevermind mathstudent got it for you :)

Answer 10

Can you simplify that now?

Answer 11

Remember we use the PEMDAS methodshere like in most algebraic equations.

Answer 12

So start by simplifying the parenthesis :)

Answer 13

@najaas You had two mistakes.
1. the first term in the quadratic formula is -b, so you need -5, not 5
2. inside the root, it's 25 - 12, not 25 + 12

Answer 14

@mathstudent55 has the right solution. @dauspex you sort of messed up.

Answer 15

so the answer is -9 and 4?

Answer 16

No.
sqrt(13) is irrational and can't be simplified.

Answer 17

\( x = \dfrac{-5 \pm \sqrt{ 25 - 12}} {2}\)

\( x = \dfrac{-5 \pm \sqrt{ 13}} {2}\)

\( x = \dfrac{-5 + \sqrt{ 13}} {2}\) or \( x = \dfrac{-5 - \sqrt{ 13}} {2}\)

Answer 18

ooh yeah, okay, I forgot about the square root

Answer 19

Remember, we let x be the smaller of the two numbers.
For each of the two solutions, you now add 5 to find the second number.
The final solution is two pairs of numbers.

Answer 20

how do you add -5 and the root of 13 ? @mathstudent55

Answer 21

You must use a common denominator:

\( \dfrac{-5 - \sqrt{ 13}} {2} + 5\)

\(= \dfrac{-5 - \sqrt{ 13}} {2} + \dfrac{5 \times 2}{2}\)

\(= \dfrac{-5 - \sqrt{ 13}} {2} + \dfrac{10}{2}\)

\(= \dfrac{5 - \sqrt{ 13}} {2} \)

Answer 22

Then you do the same for the other solution.

Answer 23

okay, thanks @mathstudent55