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Answer:

x= -2 or x= 8

Step-by-step explanation:

[tex]x^{2} - 6x + 9 = 25[/tex]

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

[tex]x^{2} -6x + 9 - 25 = 0[/tex]

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

[tex]x^{2} - 6x - 16 = 0[/tex]

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.

[tex](x - 8)(x + 2) = 0[/tex]

Seperate both equations.

[tex]x - 8 = 0 \\ x + 2 = 0[/tex]

Find the value of both x.

[tex]x = 8 \\ x = - 2[/tex]

The answer is x = -2, 8

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

The value of x in the equation [tex]x^{2} - 6x + 9 = 25[/tex] is x = -2 and x = 8.

We have to determine, the values of x in the equation [tex]x^{2} - 6x + 9 = 25.[/tex].

According to the question,

The roots of a polynomial are called its zeroes. It is because the roots are the x values at which the function is equal to zero.

A polynomial is an expression that has two or more algebraic terms.

Therefore,

The value of x for the equation,

[tex]x^{2} -6x + 9 = 25\\\\x^{2} -6x + 9-25=0\\\\x^{2} -6x - 16=0\\\\x^{2} -8x+2x-16=0\\\\x ( x-8) + 2(x-16)\\\\(x-8) (x+2)\\\\Then, \ x - 8 = 0 , \ x= 8\\\\And \ x + 2= 0 , \ x=-2[/tex]

Hence, The value of x in the equation [tex]x^{2} - 6x + 9 = 25[/tex] is x = -2 and x = 8.

To know more about the Quadratic equation click the link given below.

https://brainly.com/question/18175386

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