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
