Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

Question

X^2-6=x

Answer 1

To use the quadratic formula, we first need to get the equation in the form ax^2 + bx + c = 0. So we'll start by moving the 6 over to the other side:

x^2 - x - 6 = 0

Now we can identify our values:

a = 1
b = -1
c = -6

Plugging these into the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

x = (-(-1) ± √((-1)^2 - 4(1)(-6))) / 2(1)

x = (1 ± √(25)) / 2

x = (1 ± 5) / 2

x = 3 or x = -2

So our solutions are x = 3 and x = -2.

Answer 2

Which you can check with
x^2 - x - 6 = 0
(x- 3)(x+2) = 0
x = 3 and x = -2

Answer 3

That's correct! We can check our solutions by plugging them back into the original equation and seeing if we get 0:

For x = 3:
x^2 - x - 6 = 0
3^2 - 3 - 6 = 0
9 - 3 - 6 = 0
0 = 0

So x = 3 is indeed a solution.

For x = -2:
x^2 - x - 6 = 0
(-2)^2 - (-2) - 6 = 0
4 + 2 - 6 = 0
0 = 0

So x = -2 is also a solution.