How do you solve y = x^2 - 16x + 58 using the quadratic formula?

2 Answers
Mar 6, 2018

x=8+-sqrt(6)

Explanation:

Quadratic Formula:

For every Ax^2+Bx+C=0,

x=[-B+-sqrt(B^2-4AC)]/(2A)

For the equation x^2-16x+58=0

x=[-(-16)+-sqrt((-16)^2-4(1)(58))]/(2(1))

x=[16+-sqrt(256-232)]/2

x=[16+-sqrt(24)]/2

x=[16+-2sqrt(6)]/2

x=8+-sqrt(6)

Note: the sign +- means that both addition and subtraction gives answers, in this case, the two roots are 8+sqrt6 and 8-sqrt6.

Mar 6, 2018

8+-sqrt(6)

which would mean 8+sqrt(6) and 8-sqrt(6) are your two solutions.

Explanation:

Alright, so our quadratic formula is

x_(1,2) = (-b +- sqrt(b^2-4ac))/(2a)

So our a, b, and c values are all the leading coefficients, so (1,-16,58)

Next step: insert the numbers into the formula (double negative makes the 16 positive)

x_(1,2) = (-(-16)+- sqrt(-16^2-4(1)(58)))/(2(1))

x_(1,2) = (8+-sqrt(24))/(2)

Now we can simplify our square root by doing

sqrt(24) = 2sqrt(6)

The two's will now cancel out on the top and bottom and we will be left with

x_(1,2) = 8+- sqrt(6)