A quadratic equation can be solved by taking the square root of both sides of the equation. This method uses the square root property,

Before taking the square root, the equation must be arranged with the x2 term isolated on the left- hand side of the equation and its coefficient reduced to 1. There are four steps in solving quadratic equations by this method:

**Step 1:** Isolate the and terms. Use the addition and subtraction and isolate the and terms on the left-hand side of the equation. Then, use the multiplication and division axioms to eliminate the coefficient from the term.

**Step 2:** Make the coefficient on the term equal to . Use multiplication or division to eliminate the coefficient from the term.

**Step 3:** Complete the square. To complete the square, take the coefficient of the term, square it, and divide it by 4.

**Step 4:** Solve the equation in step 3 by taking the square root of both sides of the equation.

**Example 1:**

Step 1: Isolate the and terms.

Step 2: Make the coefficient on the term equal to .\\

It is already .

Step 3: Complete the square.

Step 4: Solve the equation in step 3 by taking the square root of both sides of the equation.

**Example 2:**

Step 1: Isolate the and terms.

Step 2: Make the coefficient on the term equal to .\\

It is already .

Step 3: Complete the square.

Step 4: Solve the equation in step 3 by taking the square root of both sides of the equation.

**Example 3:**

Step 1: Isolate the and terms.

Step 2: Make the coefficient on the term equal to .\\

Step 3: Complete the square.

Step 4: Solve the equation in step 3 by taking the square root of both sides of the equation.

**Example 4:**

Step 1: Isolate the and terms.

Step 2: Make the coefficient on the term equal to .\\

Step 3: Complete the square.

Step 4: Solve the equation in step 3 by taking the square root of both sides of the equation.

I’m confused about step 3 in example 1. You’ve added 16 to both sides, which I assume you got from squaring the coefficient of the

xterm, 4. But shouldn’t you then divide 16 by 4, so that you add 4 to both sides? I don’t understand how (x+ 4)^2 is the same asx^2 + 4x+ 16.Hi Rob,

I apologize, my solution was wrong. I also changed the problem from to (just to have real answers)