# Common Core: High School - Algebra : Use Completing the Square to Derive the Quadratic Formula: CCSS.Math.Content.HSA-REI.B.4a

## Example Questions

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### Example Question #1 : Use Completing The Square To Derive The Quadratic Formula: Ccss.Math.Content.Hsa Rei.B.4a

Solve  by completing the square. Round your answer to the nearest hundredth.

Explanation:

The first step is to add  to both sides.

Now we take the coefficient in front of the  term, divide it by , square it and add it to each side.

Now we factor the left hand side, and add up the right hand side.

Now we take the square root of each side.

Now we subtract  from each side.

Since we are taking the square root, we need to set up  equations to solve for .

### Example Question #2 : Use Completing The Square To Derive The Quadratic Formula: Ccss.Math.Content.Hsa Rei.B.4a

Solve  by completing the square. Round your answer to the nearest hundredth.

Explanation:

The first step is to add  to both sides.

Now we take the coefficient in front of the  term, divide it by , square it and add it to each side.

Now we factor the left hand side, and add up the right hand side.

Now we take the square root of each side.

Now we subtract  from each side.

Since we are taking the square root, we need to set up  equations to solve for .

### Example Question #1 : Use Completing The Square To Derive The Quadratic Formula: Ccss.Math.Content.Hsa Rei.B.4a

Solve  by completing the square. Round your answer to the nearest hundredth.

Explanation:

The first step is to add  to both sides.

Now we take the coefficient in front of the  term, divide it by , square it and add it to each side.

Now we factor the left hand side, and add up the right hand side.

Now we take the square root of each side.

Now we subtract  from each side.

Since we are taking the square root, we need to set up  equations to solve for .

### Example Question #4 : Use Completing The Square To Derive The Quadratic Formula: Ccss.Math.Content.Hsa Rei.B.4a

Solve  by completing the square. Round your answer to the nearest hundredth.

Explanation:

The first step is to add  to both sides.

Now we take the coefficient in front of the  term, divide it by , square it and add it to each side.

Now we factor the left hand side, and add up the right hand side.

Now we take the square root of each side.

Now we subtract  from each side.

Since we are taking the square root, we need to set up  equations to solve for .

### Example Question #2 : Use Completing The Square To Derive The Quadratic Formula: Ccss.Math.Content.Hsa Rei.B.4a

Solve  by completing the square. Round your answer to the nearest hundredth.

Explanation:

The first step is to add  to both sides.

Now we take the coefficient in front of the  term, divide it by , square it and add it to each side.

Now we factor the left hand side, and add up the right hand side.

Now we take the square root of each side.

Now we subtract  from each side.

Since we are taking the square root, we need to set up  equations to solve for .

### Example Question #6 : Use Completing The Square To Derive The Quadratic Formula: Ccss.Math.Content.Hsa Rei.B.4a

Solve  by completing the square. Round your answer to the nearest hundredth.

Explanation:

The first step is to add  to both sides.

Now we take the coefficient in front of the  term, divide it by , square it and add it to each side.

Now we factor the left hand side, and add up the right hand side.

Now we take the square root of each side.

Now we subtract  from each side.

Since we are taking the square root, we need to set up  equations to solve for .

### Example Question #3 : Use Completing The Square To Derive The Quadratic Formula: Ccss.Math.Content.Hsa Rei.B.4a

Solve  by completing the square. Round your answer to the nearest hundredth.

Explanation:

The first step is to add  to both sides.

Now we take the coefficient in front of the  term, divide it by , square it and add it to each side.

Now we factor the left hand side, and add up the right hand side.

Now we take the square root of each side.

Now we subtract  from each side.

Since we are taking the square root, we need to set up  equations to solve for .

### Example Question #4 : Use Completing The Square To Derive The Quadratic Formula: Ccss.Math.Content.Hsa Rei.B.4a

Solve  by completing the square. Round your answer to the nearest hundredth.

Explanation:

The first step is to add  to both sides.

Now we take the coefficient in front of the  term, divide it by , square it and add it to each side.

Now we factor the left hand side, and add up the right hand side.

Now we take the square root of each side.

Now we subtract  from each side.

Since we are taking the square root, we need to set up  equations to solve for .

### Example Question #9 : Use Completing The Square To Derive The Quadratic Formula: Ccss.Math.Content.Hsa Rei.B.4a

Solve  by completing the square. Round your answer to the nearest hundredth.

Explanation:

The first step is to add 40 to both sides.

Now we take the coefficient in front of the  term, divide it by , square it and add it to each side.

Now we factor the left hand side, and add up the right hand side.

Now we take the square root of each side.

Now we subtract  from each side.

Since we are taking the square root, we need to set up  equations to solve for .

### Example Question #10 : Use Completing The Square To Derive The Quadratic Formula: Ccss.Math.Content.Hsa Rei.B.4a

Solve  by completing the square. Round your answer to the nearest hundredth.

Explanation:

The first step is to add  to both sides.

Now we take the coefficient in front of the  term, divide it by , square it and add it to each side.

Now we factor the left hand side, and add up the right hand side.

Now we take the square root of each side.

Now we subtract  from each side.

Since we are taking the square root, we need to set up  equations to solve for .

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