Question

Solve the equation by using the quadratic formula. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)
x^2 - 8x = 2

Answer 1

subtract 2 from both sides to get

x^2 - 8x - 2

now, when it comes to the quadratic formula, you have three important numbers: a, b, and c

a is the coefficient of x^2 (in your case, a = 1)
b is the coefficient of x (b = -8)
c is the constant -2

here's the quadratic formula

https://magoosh.com/math/files/2018/06/402px-Quadratic_formula.svg_.png

now, it involves a square root: if the part under the square root (b^2 - 4ac, also called the discriminant) is negative, you can stop there (no real solution). otherwise, keep simplifying until you get your roots.

Answer 2

important: your quadratic equation needs to be in ax^2 + bx + c = 0 form otherwise your a/b/c will be incorrect

Answer 3

thanks for the explanation @vocaloid, definitely helped me get started. i'm not sure where to go from here though

Answer 4

i can't play .heic files on my computer ;-; do you have any other way to show me where you are?

Answer 5

hey yeah sorry, here!

Answer 6

arithmetic is good so far

you can make the -(-8) a positive 8

for sqrt(72), you can re-write this as sqrt(36*2). since sqrt(36) = 6, you can re-write this as 6sqrt(2)

from there you have (4 +/- 6sqrt(2)) / 2

since you have the numerator divided by 2, you can divide to get 4 +/- 3sqrt(2), making 4 + 3sqrt(2) and 4 - 3sqrt(2) as your roots

Answer 7

sorry, why did we divide the 8 by 2 before we divided the 6 sq rt 2?

Answer 8

and is that what the plus or minus sign means? that we will have 2 roots?

Answer 9

ah, sorry that was my mistake

you can make the -(-8) a positive 8

for sqrt(72), you can re-write this as sqrt(36*2). since sqrt(36) = 6, you can re-write this as 6sqrt(2)

from there you have (8 +/- 6sqrt(2)) / 2

since you have the numerator divided by 2, you can divide to get 4 +/- 3sqrt(2), making 4 + 3sqrt(2) and 4 - 3sqrt(2) as your roots

Answer 10

should be positive 8 in that third line not 4

Answer 11

yes, plus/minus means 2 roots

so you take the + version and the - version as separate roots

Answer 12

gotchya! that makes a lot of sense, thank you so much.

Answer 13

the problem also asks to provide an answer rounded to two decimal points, how do i do that?

Answer 14

plug them into a calculator

4 + 3sqrt(2) = approx 8.24
4 - 3sqrt(2) = approx -0.24

Answer 15

thank you @vocaloid ! appreciate it, definitely helped a lot