3. Solve for the zeros. Use the Completing the Square method.
a) f(x) = x2 – 18x + 53

Step-by-step explanation:

To solve a quadratic equation by completing squares we need to recall these basic algebra relations called the square of a binomial:

We can use them from right to left to factor trinomials:

We need to solve the equation:

Subtracting 53:

The first two terms of the left side of the equation are the first two terms of the trinomial given in the formula, having:

Or, equivalently:

Also:

Since a=x

Simplifying:

b=-9

We need to complete the square by adding

Adding 81:

Factoring and operating:

Since 28=4*7

Taking square roots:

Separating the square root of 4:

Solving:

The two solutions are:

a=24; b=12

step-by-step explanation:

a/b=2: 1

a=2b

36/(1+2)=12

b=12

a=24