Solve by completing the square

Question

2x^2+49=-20x 

Answer 1

(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)     √

Answer 2

2x² + 49 = -20x

 

2x² + 20x + 49 = 0

 

x² + 10x + 49/2 = 0

 

x² + 10x  = -49/2

 

x² + 10x + 25 = 25 - 49/2

 

x² + 10x + 25 = 1/2

 

(x + 5)² = 1/2

 

x + 5 = ±√(1/2)

 

x = -5 ±√(2)/2

 

x = -5 ± 0.707  [-4.293, -5.707]