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Math Help - Make a perfect square

  1. #1
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    Make a perfect square

    I need to make 8x^2+36x a perfect square, which number would i add to it to do so?(this is for parametric sequences in calc 2, but i just need to know the number i use to make that part a perfect square)
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  2. #2
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    The idea here is that you want to write an equation such that a^2x^2 + bx + c^2 = (ax + c)^2, so you have to come up with a way to solve for c and c^2. In this case you want to know c^2.One thing we know about squaring an polynomial of the form (ax + c) is that b from above can be given by b = 2ac. Therefore in your case you can solve for c and square it to get the value you need, i.e. solve for c in the following and then square the result
     36 = 2\sqrt{8}c\Rightarrow36^2 = 4\cdot 8 \cdot c^2
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  3. #3
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    Post you need to add

    here for the given problem if we add 41 it will make a perfect square

    8x2+36x+41
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  4. #4
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    Quote Originally Posted by upender View Post
    here for the given problem if we add 41 it will make a perfect square

    8x2+36x+41
    For that equation b^2-4ac=-16 so it will be ok in \mathbb{C} but I think the OP wants a real solution

    I'd use the discriminant to find c. For it to be a perfect square we know that b^2-4ac=0

    36^2 = 4 \times 8 \times c

    c = \frac{36^2}{32} = 40.5
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