Find the solutions to the equation by compelting the square x^2-6x=7

To complete the square x^2-6x=7

We take the coefficient of X which is - 6

divide it by 2 - 3

square that number 9

then add it to both sides of the equation.

x^2 - 6x + 9 = 16

(x - 3) * (x - 3) = 16

We take the square root of both sides:

a) x-3 = 4

b) x-3 = - 4

Therefore, x = 7 and x = - 1

The solution set is {-1, 7}

Step-by-step explanation:

Rewrite x^2-6x=7 as x^2 - 6x = 7.

Identify the coefficient of the x term; it is - 6.

Halve this coeff (obtaining - 3)

Square this result (obtaining 9)

Add 9 to x^2 - 6x and then subtract 9 from the result: x^2 - 6x + 9 - 9

Then we have:

x^2 - 6x + 9 - 9 = 7. Add 9 to both sides, obtaining

x^2 - 6x + 9 = 16

Rewrite x^2 - 6x + 9 as the square of a binomial: (x - 3) ^2

Then we have

(x - 3) ^2 = 16

Taking the square root of both sides, we get

x - 3 = ±4, so that: x = 3 + 4 = 7, and x = 3 - 4 = - 1.

The solution set is {-1, 7}.