Solve x^2 -6x=-5 by completing the square. Show all work for the steps below. (a) For x^2 -6x+c+-5+c, what value of c is used to complete the square? (b) Substitute the value for c in Part 2(a). Then complete the square to rewrite the equation as the square of a binomial. (c) Solve for x

X^2 - 6x = -5

To complete the square we are going to rewrite the equation to a quadratic equation in the form:

ax² + bx + c

To do this we are going to transpose.

x² - 6x = -5
x² - 6x + 5 = 0

Now we are going to rewrite the new equation in the form

a(x + h)² + k

Where a = 1
h = 6x
k = 5

1(x² - 6x) + 5 = 0
1(x² - 6x/2 + 3²) + 5 = 0, to find h, divide it by 2 then square the quotient and add it to the equation.

1(x² - 3x + 9) + 5 - 9 = 0, to find k, subtract the square rooted quotient after multiplying it by a.

1(x - 3)²- 4 = 0

Now we solve.

1(x - 3)² - 4 = 0
1(x - 3)² = 4
±√1(x - 3)² = ±√4
(x - 3) = √4 or (x - 3) = -√4
x = 5 or x = 1