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Which equation is equivalent to the given equation?

[tex]\[ x^2 - 6x = 8 \][/tex]

A. [tex]\((x-6)^2 = 20\)[/tex]

B. [tex]\((x-6)^2 = 44\)[/tex]

C. [tex]\((x-3)^2 = 14\)[/tex]

D. [tex]\((x-3)^2 = 17\)[/tex]

Sagot :

GinnyAnsweridn
To determine which equation is equivalent to the given equation [tex]\( x^2 - 6x = -8 \)[/tex], we will complete the square. Follow these steps:

1. Start with the given equation:
[tex]\[ x^2 - 6x = -8 \][/tex]

2. To complete the square, we need to form a perfect square trinomial on the left side. Begin by isolating the quadratic and linear terms:
[tex]\[ x^2 - 6x \][/tex]

3. Take the coefficient of [tex]\( x \)[/tex], which is [tex]\(-6\)[/tex], divide it by 2, and square the result:
[tex]\[ \left(-\frac{6}{2}\right)^2 = 9 \][/tex]

4. Add and subtract this square (9) inside the equation to keep it balanced:
[tex]\[ x^2 - 6x + 9 - 9 = -8 \][/tex]

5. Rewrite the perfect square trinomial as a square of a binomial:
[tex]\[ (x - 3)^2 - 9 = -8 \][/tex]

6. Move the constant term [tex]\(-9\)[/tex] to the other side of the equation:
[tex]\[ (x - 3)^2 - 9 = -8 \][/tex]
[tex]\[ (x - 3)^2 = -8 + 9 \][/tex]
[tex]\[ (x - 3)^2 = 1 \][/tex]

Now compare this with the provided answer choices. None match. So it looks like there's an error in given options, since correct answer doesn't match any.
Wegnerkolmp2741oidn

Answer:

D. (x-3)^2 = 17

Step-by-step explanation:

Which equation is equivalent to the given equation?

x^2 - 6x = 8

Complete the square by adding a term to each side of the equation

Take -6.

Divide by 2.

-6/2= -3

Square it.

(-3) ^2 = 9

Add 9 to each side

x^2 - 6x+9 = 8+9

Factor the left side

(x-3) ^2 = 17

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