Completing the Square

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Completing the Square

• A Guide to Solving Quadratic Equations

Heidi Wieland Class of 2007
2-9-07
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The method of transforming a quadratic equation
so that one side is a perfect trinomial is called
completing the square.
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Solve 2x2-12x-70

• First, divide the entire problem by 2. This
  gives you
• x2-6x-7/20
• Next, subtract the constant term from both
  sides. You should have
• x2-6x7/2

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x2-6x7/2

• Add the square of half of the middle term ( the
  middle term is 6, so half would be 3, then square
  it) to each side of the equation.
• x2-6x97/29

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x2-6x97/29

• Simplify your equation.
• x2-6x925/2
• Now, carry the x and half of the middle term
  (6), put them in parentheses, and square it.
• (x-3)2
• Your equation is now (x-3)225/2

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(x-3)225/2

• Square root both sides of the problem. The
  equation is now
• x-3 the square root of 25/2.
• Move the 3 to the other side of the equation.

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• The square root of 25 is 5, so our equation is 5
• A fraction cant be inside a square root. So,
  we multiply the square root by itself to get rid
  of the fraction.
• 5

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• The square root of 2 times itself equals 2.
  Therefore, your equation is
• x3 5
• 2
• You have now completed the square!