You must add 9/4 in order to make this a perfect square.

Steps to Solving Equations by Completing the Square

1. Rewrite the equation in the form x2 + bx = c.
2. Add to both sides the term needed to complete the square.
3. Factor the perfect square trinomial.
4. Solve the resulting equation by using the square root property.

1. Step 1: Rearrange–Divide (as needed)
2. Step 2: Half–Square–Add.
3. Step 3: Factor Left–Simplify Right.
4. Step 4: Solve!
5. Step 1: Divide & Group, Move Constant Rt.
6. Step 1: Group & Factor.
7. Step 2: Complete the Square Twice, (Add)
8. Step 2: Complete the Square, (Add-Mult.-Subtract)

Example 1. We’re given a quadratic and asked to complete the square. We begin by moving the constant term to the right side of the equation. We complete the square by taking half of the coefficient of our x term, squaring it, and adding it to both sides of the equation.

In order to use the Completing the Square method, the value for a in the quadratic equation must be 1 . If it is not 1 , you will have to use the AC method or the quadratic formula in order to solve for x .

64

so the answer is 4.

“The correct answer is 36.

The answer is 36.

What number should be added to the expression to change it into a perfect square trinomial? 36. You just studied 5 terms!

Answer. Any time you take a binomial and multiply it to itself, you end up with a perfect square trinomial. For example, take the binomial (x + 2) and multiply it by itself (x + 2). The result is a perfect square trinomial.

In a perfect square trinomial, two of your terms will be perfect squares. For example, in the trinomial x2 – 12x + 36, both x2 and 36 are perfect squares. The square root of x2 is x, the square root of 36 is 6, and 2 times x (which is the same as 1) times 6 equals 12x/-12x, which does equal the other term.

A perfect square trinomial is found in the expression where both the leading coefficients and the constant are both perfect squares. 16 is a perfect square of 4 times 4, and 9 is a perfect square of 3 times 3.

A perfect square is a value that has a whole number square root. The square root of 4 is 2, so it’s square root is a whole number, which means the four is a perfect square. Another example of a perfect square is 9. The square root of 9 is 3.

The perfect squares are the squares of the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 … Here are the square roots of all the perfect squares from 1 to 100. 1. Estimate – first, get as close as you can by finding two perfect square roots your number is between.

As the cube root of 27 is a whole number, 27 is a perfect cube….Cube root of 27 in radical form: ∛27.

A number is perfect if the sum of its proper factors is equal to the number. To find the proper factors of a number, write down all numbers that divide the number with the exception of the number itself. If the sum of the factors is equal to 18, then 18 is a perfect number. Therefore, 18 is not perfect.