Question

What are the values of x in the equation x2 - 6x + 9 = 25?

Answer 1

Answer:

a

Step-by-step explanation:

Answer 2

Answer:

x= -2 or x= 8

Step-by-step explanation:

$x^{2} - 6x + 9 = 25$

First step, move 25 to the left side so we can do the Quadratic Formula (or you can factor instead.)

$x^{2} -6x + 9 - 25 = 0$

Next, we know that 9-25 equals -16.

$x^{2} - 6x - 16 = 0$

Now find that what two numbers multiply and get 16: 2×8 4×4 and 16×1.

Now we do some kind of factoring. The most valuable number must be negative since -6x is negative.

Let's explain about factoring in Quadratic a little bit.

Substitue x²-6x-16 as ax²+bx+c=0

From (ax+d)(bx+c), if we multiply ax and bx, we get the ax²

If we multiply ax and c, we get acx and we multiply d and bx, we get dbx. (axc+bdx) = bx

If we multiply d and c, we get c.

From the factor lf 16, 2×8 seems to be right since -8+2 equals -6 which matches the equation.

Then we get.

$(x - 8)(x + 2) = 0$

Seperate both equations.

$x - 8 = 0 \\ x + 2 = 0$

Find the value of both x.

$x = 8 \\ x = - 2$

The answer is x = -2, 8

(The explanation might be weird since I don't know what they are called in English.)