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Solve by completing the square

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1 Answer

(a+b)^2 = a^2 + 2ab + b^2
 
So if we can generate the pattern a^2 + 2ab + b^2
we can replace it with (a+b)^2.
 
2x^2 + 49 = -20x
 
2x^2 + 20x + 49 = 0
 
2(x^2 + 10x) + 49 = 0
 
2(x^2 + 2(5)x + 5^2 - 5^2) + 49 = 0
 
2((x + 5)^2 - 5^2) + 49 = 0
 
2((x + 5)^2 - 25) + 49 = 0
 
2(x + 5)^2 - 50 + 49 = 0
 
2(x + 5)^2 = 1
 
(x + 5)^2 = 1/2 = 2/4
 
|x + 5| = (√2)/2
 
x + 5 = ±(√2)/2
 
x = -5 ± (√2)/2
 
check:
 
2x^2 + 49 =? -20x
 
2(-5 ± (√2)/2)^2 + 49 =? -20(-5 ± (√2)/2)
 
2(25 ± (-5√2) + 1/2) + 49 =? 100 ± (-10√2)
 
50 ± (-10√2) + 1 + 49 =? 100 ± (-10√2)
 
100 ± (-10√2) = 100 ± (-10√2)     √