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In what order form should an equation be in order to use the square root property and...

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In what order form should an equation be in order to use the square root property and when should the square root property be used instead of factory?

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The square root property is a method used to solve for an equation in the second degree, usually of the form `ax^2 + c = 0` . Notice that there is no `x`  in the equation. However, aside from this we can also use the square root property for quadratic equations (second degree equations) that are perfect square trinomials.` `

Examples of perfect square trinomials are:

  • `x^2 + 4x + 4 = (x+2)^2`
  • `x^2 - 6x + 9 = (x+3)^2` 

Notice that the left hand side can be expressed as a square of a term.

Examples using the square root property:

Solve for x in the following:

`5x^2 - 20 = 0`

This is equivalent to `5x^2 = 20 rarr x^2 = 20/5 = 4 rarr x^2 = 4` using the square root property: `sqrt(x^2) = pm sqrt4` Hence, `x = pm 2` .

Another one involving perfect squares:

`x^2 - 6x + 9 = 0`

We know that the left hand side is `(x-3)^2.`

Hence, we have `(x-3)^2 = 0`. Taking the root of both sides gives us `sqrt((x-3)^2) = pm sqrt(0) rarr (x-3) = 0 rarr x = 3.`

 

To your next question, factoring can be used if the equation is easily factorable. However, a more convenient way would be completing the square (general method) or the use of the quadratic formula. The square root property can also be used (and is actually used) in the process called completing the square.

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