How Do You Complete the Square?
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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)
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- How Do You Complete the Square?. (2013, March 2). In ClassBrain Math Tutorials. Retrieved 12:17, May 22, 2013, from http://www.classbrainmath.com/2010/03/solving-a-quadratic-equations-by-completing-the-square/
- MLA style
- Cynthia Kirkeby, “How Do You Complete the Square?.” ClassBrain Math Tutorials. 2 March 2013, 10:41 UTC. . 22 May 2013 <http://www.classbrainmath.com/2010/03/solving-a-quadratic-equations-by-completing-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/2010/03/solving-a-quadratic-equations-by-completing-the-square/> [accessed 22 May 2013]
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- CBE/CSE style
- Cynthia Kirkeby, How Do You Complete the Square? [Internet]. ClassBrain Math Tutorials; 2013 March 2, 10:41 UTC [cited 2013 May 22]. Available from: http://www.classbrainmath.com/2010/03/solving-a-quadratic-equations-by-completing-the-square/.
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- How Do You Complete the Square?, http://www.classbrainmath.com/2010/03/solving-a-quadratic-equations-by-completing-the-square/ (last visited May. 22, 2013).
- 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/2010/03/solving-a-quadratic-equations-by-completing-the-square/. Accessed May 22, 2013.
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3 Responses to “How Do You Complete the Square?”
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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.