Using Quadriatic Formula?

Question

I tried to solve using the Quadriatic formula and can't solve, can you help?

x^2 - 7x - 1 = -7

Answer 1

Did you remember to bring that -7 over to the other side first?  The quadratic formula assumes that your equation is in the form of ax^2 + bx + c = 0

Adding -7 to both sides gives:

x^2 - 7x + 6 = 0

This is easy to factor, but you're asking how to solve this using the quadratic formula (a fact which seems to have escaped some other answerers).  Here, a = 1, b= -7, and c = 6.  So:

x = [ 7 ± √(49 - 4(1)(6)) ] / 2(1)

x = [ 7 ± √25 ] / 2

x = [ 7 ± 5 ] / 2

x = (7+5)/2 or (7-5)/2

x = 6, 1

Answer 2

x^2 - 7x - 1 = -7

x^2 - 7x + 6 = 0

(x - 6)(x - 1) = 0

x = 1 or x = 6

Answer 3

x = 6 and x = 1

Here is how I got it:

x² - 7x - 1 = -7.  To use the quadratic formula, the equation must equal zero.  So add 7 to both sides.

x² - 7x - 1 + 7 = 0

x² - 7x + 6 = 0

The quadratic formula is x = [-b ± sqrt(b² - 4ac)] / (2a).

a = 1, b = -7, c = 6

x = [-(-7) ± sqrt((-7)² - (4 * 1 * 6))] / (2 * 1)

x = [7 ± sqrt(49 - 24)] / 2

x = [7 ± sqrt(25)] / 2

x = (7 ± 5) / 2

x = (7 + 5) / 2, (7 - 5) / 2

x = 12/2, 2/2

x = 6, 1

Answer 4

x^2-7x-1=-7 (original)

x^2-7x-1+7=0 (set equation to standard form by making it equal 0)

x^2-7x+6=0

x=[-b+/-_/(b^2-4ac)]/2a

Sub a=1 b=-7 c=6

x=[7+/-_/(49-24)]/2 (subbed in and simplified a bit)

x=(7+/-5)/2 (simplified and skipped a bunch of simple steps)

so x=(7-5)/2=1

or x=(7+5)/2=6