



 
Hi Rebecca. I'll show you an example and then you can use this method to solve your questions. Example: Find the roots of 2x² + 16x + 20 by completing the square. Completing the square means we want to make a perfect square as we do this. We'll solve for it using the equation 2x² + 16x + 20 = 0 First things first though: simplify the numbers if you can! 2 goes into everything, so it reduces to just: x² + 8x + 10 = 0 I start by moving the constant (third) term to the other side: x² + 8x = 10 Now I want the left hand side to become a perfect square. The way I do that is by taking half the coefficient of the x term (that is, one half of 8, which is 4) and then squaring that (to make 16). I add this to both sides of the equation: x² + 8x + 16 = 10 + 16 The left hand side is now a perfect square. It's the perfect square of x and half of +8 (which is 4). So I can rewrite this as: (x + 4)² = 6 Now I take the square root of both sides. That just cancels out the squared on the left side. Remember that there is both a positive and negative square root! x + 4 = ±√6 I solve for x: x = ±√6  4 So this is actually two numbers (because of that ± sign). The two roots are: x = √6  4 Now my example is done. I hope you can see how to do your problems now, step by step. Cheers,  


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