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Solving quadratics can be difficult. Completing the square is one method for solving a quadratic equation. A quadratic equation can also be solved by factoring, using the square roots, or using the quadratic formula. The cool thing is that solving quadratic equations by completing the square *will always work* when solving quadratic equations, and the technique is a good tool to have in your math tool belt.

### How Do You Complete the Square?

This video is brought to you courtesy of dangarbo10 (YouTube)

### Citation styles

- APA style
- How Do You Complete the Square?. (2013, March 2). In
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- Cynthia Kirkeby, “How Do You Complete the Square?.”
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- Cynthia Kirkeby, 'How Do You Complete the Square?',
*ClassBrain Math Tutorials*, 2 March 2013, 10:41 UTC, <http://www.classbrainmath.com/solving-a-quadratic-equations-by-completing-the-square/> [accessed 22 September 2017] - The Chicago Manual of Style
- Cynthia Kirkeby, “How Do You Complete the Square?.”
*ClassBrain Math Tutorials*, http://www.classbrainmath.com/solving-a-quadratic-equations-by-completing-the-square/ [accessed September 22, 2017]. - CBE/CSE style
- Cynthia Kirkeby, How Do You Complete the Square? [Internet]. ClassBrain Math Tutorials; 2013 March 2, 10:41 UTC [cited 2017 Sep 22]. Available from: http://www.classbrainmath.com/solving-a-quadratic-equations-by-completing-the-square/.
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- AMA style
- Cynthia Kirkeby, How Do You Complete the Square?. ClassBrain Math Tutorials. March 2, 2013, 10:41 UTC. Available at: http://www.classbrainmath.com/solving-a-quadratic-equations-by-completing-the-square/. Accessed September 22, 2017.

Simplifying

4x^2 + 3x + -6 = y

Isolate the 1st 2 terms:

4x^2 + 3x + 0 = 6

Divide through by 4 to bring 1st term to x^2

x^2 + 3/4x + 0 = 6/4

Take half of the coefficient (don’t forget the sign!) of the x-term, and square it. Add this square to both sides of the equation.

x^2 + 3/4x + (3/8)^2 = 6/4 + (3/8)^2

Simplify

x^2 + 3/4x + 9/64 = 6/4 + 9/64

Place into standard form

(x + 3/8)^2 = 96/64 + 9/64

Combine Like terms

(x + 3/8)^2 = 105/64

Square-root both sides, remembering the “±” on the right-hand side. Simplify as necessary.

x + 3/8 = ±√105/8

Solve for x

Remember that the “±” means that you have two values for x.

x = -3/8 + √105/8

x = -3/8 – √105/8

THANK YOU! This video explained this to me better in five minutes, than my algebra two teacher has in the past week!

You are very welcome. 🙂