# complete the square to convert the 2x^2 - 20x - 48 to vertex form

mvcdc | Student, Graduate | (Level 2) Associate Educator

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We want to convert the quadratic equation from the form:

`ax^2 + bx + c = 0` to the form `a(x-h)^2 + k = 0` .

In completing the square, first group the terms containing `x.`

Hence:

`(2x^2 - 20x) - 48 = 0`

Now, we note that x should have a coefficient of 1, when we do completing the square, so we factor out 2:

`2(x^2 - 10x) - 48 = 0`

Our goal now is to make `x^2 - 10x`  a complete square. This can be done by adding `((-10)/2)^2 = 25` to it, so that we have: `x^2 - 10x + 25` . However, note that we do not want to change the value of the equation, and whatever we add inside the parenthesis must be subtracted out outside. Adding 25 inside the parenthesis is equivalent to adding 50 to the entire left hand side (due to the coefficient 2). Hence, the new equation is:``

`2(x^2 - 10x + 25) - 48 - 50 = 0`

Simplifying this gives us the vertex form:

`2(x-5)^2 - 98 = 0`