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Andru [333]
3 years ago
12

Solve this quadratic equation by completing the square. x^2+4x=15

Mathematics
1 answer:
AlekseyPX3 years ago
7 0

Answer:

x =  -2  ±sqrt( 19)

Step-by-step explanation:

x^2 + 4x = 15

Take the coefficient of x

4

Divide by 2

4/2 =2

Square it

2^2 = 4

Add it to each side

x^2 + 4x+4 = 15+4

(x+2)^2 = 19

Take the square root of each side

sqrt( (x+2)^2) =±sqrt( 19)

x+2 =  ±sqrt( 19)

Subtract 2 from each side

x+2-2 = -2  ±sqrt( 19)

x =  -2  ±sqrt( 19)

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Answer:

Step-by-step explanation:

The numbers are 11 & 12

Explanation:

Let the first number be f and the second |number be s

Now the square of first No. is 23 less than the square of second No.

ie.  f 2 + 23 = s 2 . . . . . (1)

The second No. is 1 more than the first

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squaring (2), we get

( f + 1 ) 2 = s 2

expanding

f 2 + 2 ⋅ f + 1 = s 2  . . . . . (3)

Now (3) - (1) gives

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or  

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and  s = f + 1 = 11 + 1

=

12

So the numbers are 11 & 12

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